Pub Date : 2020-09-17DOI: 10.1103/PhysRevD.103.126012
Georgios Kalamakis, R. Leigh, A. Petkou
In this paper we consider aspects of the holographic interpretation of Taub-NUT-AdS$_4$. We review our earlier results which show that TNAdS$_4$ gives rise to a holographic three-dimensional conformal fluid having constant vorticity. We then study the holographic relevance of the Misner string by considering bulk scalar fluctuations. The scalar fluctuations organize naturally into representations of the $SU(2)times mathbb{R}$ isometry algebra. If we require the string's invisibility we obtain a Dirac-like quantization relating the frequency of the scalar field modes to the NUT charge. As the latter quantity determines the total vorticity flux of the boundary fluid, we argue that such an assumption allows for a holographic interpretation of TNAdS$_4$ as a {it non-dissipative} superfluid whose excitations are quantized vortices. Alternatively, if we regard the Misner string as a physical object, as has recently been advocated for thermodynamically, the aforementioned quantization conditions are removed, and we find that TNAdS$_4$ corresponds to a holographic fluid whose dissipative properties are probed as usual by the complex quasinormal modes of the bulk fluctuations. We show that such quasinormal modes are, perhaps surprisingly, organized into infinite-dimensional non-unitary representations of the isometry algebra.
{"title":"Aspects of holography of Taub-NUT-\u0000AdS4\u0000 spacetimes","authors":"Georgios Kalamakis, R. Leigh, A. Petkou","doi":"10.1103/PhysRevD.103.126012","DOIUrl":"https://doi.org/10.1103/PhysRevD.103.126012","url":null,"abstract":"In this paper we consider aspects of the holographic interpretation of Taub-NUT-AdS$_4$. We review our earlier results which show that TNAdS$_4$ gives rise to a holographic three-dimensional conformal fluid having constant vorticity. We then study the holographic relevance of the Misner string by considering bulk scalar fluctuations. The scalar fluctuations organize naturally into representations of the $SU(2)times mathbb{R}$ isometry algebra. If we require the string's invisibility we obtain a Dirac-like quantization relating the frequency of the scalar field modes to the NUT charge. As the latter quantity determines the total vorticity flux of the boundary fluid, we argue that such an assumption allows for a holographic interpretation of TNAdS$_4$ as a {it non-dissipative} superfluid whose excitations are quantized vortices. Alternatively, if we regard the Misner string as a physical object, as has recently been advocated for thermodynamically, the aforementioned quantization conditions are removed, and we find that TNAdS$_4$ corresponds to a holographic fluid whose dissipative properties are probed as usual by the complex quasinormal modes of the bulk fluctuations. We show that such quasinormal modes are, perhaps surprisingly, organized into infinite-dimensional non-unitary representations of the isometry algebra.","PeriodicalId":8443,"journal":{"name":"arXiv: High Energy Physics - Theory","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83054753","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-09-15DOI: 10.1103/physrevd.102.126009
Mariana Carrillo-González, Kurt Hinterbichler, J. Stokes, M. Trodden
We holographically calculate two-point functions in the pseudo-conformal universe, an early universe alternative to inflation. The pseudo-conformal universe can be modeled as a defect conformal field theory, where the reheating surface is a codimension-1 spacelike defect which breaks the conformal algebra to a de Sitter subalgebra. The dual spacetime geometries are domain walls with de-Sitter symmetry in an asymptotically anti-de Sitter spacetime. We compute 2-point functions of scalars and stress tensors by solving the linearized equations for scalar and tensor fluctuations about these backgrounds.
{"title":"Holographic two-point functions in the pseudoconformal universe","authors":"Mariana Carrillo-González, Kurt Hinterbichler, J. Stokes, M. Trodden","doi":"10.1103/physrevd.102.126009","DOIUrl":"https://doi.org/10.1103/physrevd.102.126009","url":null,"abstract":"We holographically calculate two-point functions in the pseudo-conformal universe, an early universe alternative to inflation. The pseudo-conformal universe can be modeled as a defect conformal field theory, where the reheating surface is a codimension-1 spacelike defect which breaks the conformal algebra to a de Sitter subalgebra. The dual spacetime geometries are domain walls with de-Sitter symmetry in an asymptotically anti-de Sitter spacetime. We compute 2-point functions of scalars and stress tensors by solving the linearized equations for scalar and tensor fluctuations about these backgrounds.","PeriodicalId":8443,"journal":{"name":"arXiv: High Energy Physics - Theory","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76030287","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-09-14DOI: 10.1103/PHYSREVD.103.044060
Samuel Brensinger, K. Heitritter, V. Rodgers, K. Stiffler
Thomas-Whitehead (TW) gravity is a projectively invariant model of gravity over a d-dimensional manifold that is intimately related to string theory through reparameterization invariance. Unparameterized geodesics are the ubiquitous structure that ties together string theory and higher dimensional gravitation. This is realized through the projective geometry of Tracy Thomas. The projective connection, due to Thomas and later Whitehead, admits a component that in one dimension is in one-to-one correspondence with the coadjoint elements of the Virasoro algebra. This component is called the diffeomorphism field $mathcal{D}_{ab }$ in the literature. It also has been shown that in four dimensions, the TW action collapses to the Einstein-Hilbert action with cosmological constant when $mathcal{D}_{ab}$ is proportional to the Einstein metric. These previous results have been restricted to either particular metrics, such as the Polyakov 2D metric, or were restricted to coordinates that were volume preserving. In this paper, we review TW gravity and derive the gauge invariant TW action that is explicitly projectively invariant and general coordinate invariant. We derive the covariant field equations for the TW action and show how fermionic fields couple to the gauge invariant theory. The independent fields are the metric tensor $g_{ab}$, the fundamental projective invariant $Pi^{a}_{,,,bc}$, and the diffeomorphism field $mathcal D_{ab}$.
{"title":"General structure of Thomas-Whitehead gravity","authors":"Samuel Brensinger, K. Heitritter, V. Rodgers, K. Stiffler","doi":"10.1103/PHYSREVD.103.044060","DOIUrl":"https://doi.org/10.1103/PHYSREVD.103.044060","url":null,"abstract":"Thomas-Whitehead (TW) gravity is a projectively invariant model of gravity over a d-dimensional manifold that is intimately related to string theory through reparameterization invariance. Unparameterized geodesics are the ubiquitous structure that ties together string theory and higher dimensional gravitation. This is realized through the projective geometry of Tracy Thomas. The projective connection, due to Thomas and later Whitehead, admits a component that in one dimension is in one-to-one correspondence with the coadjoint elements of the Virasoro algebra. This component is called the diffeomorphism field $mathcal{D}_{ab }$ in the literature. It also has been shown that in four dimensions, the TW action collapses to the Einstein-Hilbert action with cosmological constant when $mathcal{D}_{ab}$ is proportional to the Einstein metric. These previous results have been restricted to either particular metrics, such as the Polyakov 2D metric, or were restricted to coordinates that were volume preserving. In this paper, we review TW gravity and derive the gauge invariant TW action that is explicitly projectively invariant and general coordinate invariant. We derive the covariant field equations for the TW action and show how fermionic fields couple to the gauge invariant theory. The independent fields are the metric tensor $g_{ab}$, the fundamental projective invariant $Pi^{a}_{,,,bc}$, and the diffeomorphism field $mathcal D_{ab}$.","PeriodicalId":8443,"journal":{"name":"arXiv: High Energy Physics - Theory","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85036074","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-09-12DOI: 10.1142/S0217751X21500743
J. Gamboa, J. López-Sarrión
Spontaneous symmetry breaking is studied in the ultralocal limit of a scalar quantum field theory, that is when $Eapprox m$ (or infrared limit). In this limit we show that a $ varphi^4$ theory in the euclidean space in four-dimensions describes naturally instantons. Furthermore, in the infrared limit we show that there is an exact map between $ varphi^4$ with self-dual Yang-Mills theories. The spontaneous symmetry breaking in the infrared limit for a Higgs portal is also considered and we demonstrate how states of higher energy becomes unstable and spread converting a false vacuum in a true one.
{"title":"Nonperturbative aspects of spontaneous symmetry breaking","authors":"J. Gamboa, J. López-Sarrión","doi":"10.1142/S0217751X21500743","DOIUrl":"https://doi.org/10.1142/S0217751X21500743","url":null,"abstract":"Spontaneous symmetry breaking is studied in the ultralocal limit of a scalar quantum field theory, that is when $Eapprox m$ (or infrared limit). In this limit we show that a $ varphi^4$ theory in the euclidean space in four-dimensions describes naturally instantons. Furthermore, in the infrared limit we show that there is an exact map between $ varphi^4$ with self-dual Yang-Mills theories. The spontaneous symmetry breaking in the infrared limit for a Higgs portal is also considered and we demonstrate how states of higher energy becomes unstable and spread converting a false vacuum in a true one.","PeriodicalId":8443,"journal":{"name":"arXiv: High Energy Physics - Theory","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90561772","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-09-10DOI: 10.1142/S0217751X21501062
H. Sonoda
We consider the multiple products of relevant and marginal scalar composite operators at the Gaussian fixed-point in $D=4$ dimensions. This amounts to perturbative construction of the $phi^4$ theory where the parameters of the theory are momentum dependent sources. Using the exact renormalization group (ERG) formalism, we show how the scaling properties of the sources are given by the short-distance singularities of the multiple products.
{"title":"The operator algebra at the Gaussian fixed-point","authors":"H. Sonoda","doi":"10.1142/S0217751X21501062","DOIUrl":"https://doi.org/10.1142/S0217751X21501062","url":null,"abstract":"We consider the multiple products of relevant and marginal scalar composite operators at the Gaussian fixed-point in $D=4$ dimensions. This amounts to perturbative construction of the $phi^4$ theory where the parameters of the theory are momentum dependent sources. Using the exact renormalization group (ERG) formalism, we show how the scaling properties of the sources are given by the short-distance singularities of the multiple products.","PeriodicalId":8443,"journal":{"name":"arXiv: High Energy Physics - Theory","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86078335","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-09-10DOI: 10.1103/PHYSREVX.11.011063
Shlomo S. Razamat, D. Tong
In principle, there is no obstacle to gapping fermions preserving any global symmetry that does not suffer a 't Hooft anomaly. In practice, preserving a symmetry that is realised on fermions in a chiral manner necessitates strong coupling dynamics. We show how this can be achieved using familiar results about supersymmetric gauge theories and, in particular, the phenomenon of confinement without chiral symmetry breaking. We present simple models that gap fermions while preserving a symmetry group under which they transform in chiral representations. For example, we show how to gap a collection of 4d fermions that carry the quantum numbers of one generation of the Standard Model, but without breaking electroweak symmetry. We further show how to gap fermions in groups of 16 while preserving certain discrete symmetries that exhibit a mod 16 anomaly.
{"title":"Gapped Chiral Fermions","authors":"Shlomo S. Razamat, D. Tong","doi":"10.1103/PHYSREVX.11.011063","DOIUrl":"https://doi.org/10.1103/PHYSREVX.11.011063","url":null,"abstract":"In principle, there is no obstacle to gapping fermions preserving any global symmetry that does not suffer a 't Hooft anomaly. In practice, preserving a symmetry that is realised on fermions in a chiral manner necessitates strong coupling dynamics. We show how this can be achieved using familiar results about supersymmetric gauge theories and, in particular, the phenomenon of confinement without chiral symmetry breaking. We present simple models that gap fermions while preserving a symmetry group under which they transform in chiral representations. For example, we show how to gap a collection of 4d fermions that carry the quantum numbers of one generation of the Standard Model, but without breaking electroweak symmetry. We further show how to gap fermions in groups of 16 while preserving certain discrete symmetries that exhibit a mod 16 anomaly.","PeriodicalId":8443,"journal":{"name":"arXiv: High Energy Physics - Theory","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89679005","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-09-07DOI: 10.1103/physrevd.102.125003
V. Abakumova, S. Lyakhovich
We study Hamiltonian form of unfree gauge symmetry where the gauge parameters have to obey differential equations. We consider the general case such that the Dirac-Bergmann algorithm does not necessarily terminate at secondary constraints, and tertiary and higher order constraints may arise. Given the involution relations for the first-class constraints of all generations, we provide explicit formulas for unfree gauge transformations in the Hamiltonian form, including the differential equations constraining gauge parameters. All the field theories with unfree gauge symmetry share the common feature: they admit sort of "global constants of motion" such that do not depend on the local degrees of freedom. The simplest example is the cosmological constant in the unimodular gravity. We consider these constants as modular parameters rather than conserved quantities. We provide a systematic way of identifying all the modular parameters. We demonstrate that the modular parameters contribute to the Hamiltonian constraints, while they are not explicitly involved in the action. The Hamiltonian analysis of the unfree gauge symmetry is precessed by a brief exposition for the Lagrangian analogue, including explicitly covariant formula for degrees of freedom number count. We also adjust the BFV-BRST Hamiltonian quantization method for the case of unfree gauge symmetry. The main distinction is in the content of the non-minimal sector and gauge fixing procedure. The general formalism is exemplified by traceless tensor fields of irreducible spin $s$ with the gauge symmetry parameters obeying transversality equations.
{"title":"Hamiltonian constraints and unfree gauge symmetry","authors":"V. Abakumova, S. Lyakhovich","doi":"10.1103/physrevd.102.125003","DOIUrl":"https://doi.org/10.1103/physrevd.102.125003","url":null,"abstract":"We study Hamiltonian form of unfree gauge symmetry where the gauge parameters have to obey differential equations. We consider the general case such that the Dirac-Bergmann algorithm does not necessarily terminate at secondary constraints, and tertiary and higher order constraints may arise. Given the involution relations for the first-class constraints of all generations, we provide explicit formulas for unfree gauge transformations in the Hamiltonian form, including the differential equations constraining gauge parameters. All the field theories with unfree gauge symmetry share the common feature: they admit sort of \"global constants of motion\" such that do not depend on the local degrees of freedom. The simplest example is the cosmological constant in the unimodular gravity. We consider these constants as modular parameters rather than conserved quantities. We provide a systematic way of identifying all the modular parameters. We demonstrate that the modular parameters contribute to the Hamiltonian constraints, while they are not explicitly involved in the action. The Hamiltonian analysis of the unfree gauge symmetry is precessed by a brief exposition for the Lagrangian analogue, including explicitly covariant formula for degrees of freedom number count. We also adjust the BFV-BRST Hamiltonian quantization method for the case of unfree gauge symmetry. The main distinction is in the content of the non-minimal sector and gauge fixing procedure. The general formalism is exemplified by traceless tensor fields of irreducible spin $s$ with the gauge symmetry parameters obeying transversality equations.","PeriodicalId":8443,"journal":{"name":"arXiv: High Energy Physics - Theory","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83843822","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Singular BPS boundary conditions in $$ mathcal{N} $$ = (2, 2) supersymmetric gauge theories","authors":"T. Okazaki, Douglas J. Smith","doi":"10.1007/JHEP03(2021)043","DOIUrl":"https://doi.org/10.1007/JHEP03(2021)043","url":null,"abstract":"","PeriodicalId":8443,"journal":{"name":"arXiv: High Energy Physics - Theory","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78739081","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In dieser Dissertation untersuchen wir die Niedrigenergieentwicklung von Streuamplituden geschlossener Strings auf Einschleifenniveau (d.h. auf Genus eins) in einem zehndimensionalen Minkowski-Hintergrund mit Hilfe einer speziellen Klasse von Funktionen, den sogenannten modularen Graphenformen. Diese erlauben eine systematische Berechnung der Niedrigenergieentwicklung und erfullen viele nicht-triviale algebraische- und Differentialgleichungen. Wir studieren diese Relationen detailliert und leiten Basiszerlegungen fur eine grose Zahl modularer Graphenformen her. Eines der Ergebnisse dieser Dissertation ist ein Mathematica-Paket, welches diese Vereinfachungen automatisiert. Wir benutzen diese Techniken, um die fuhrenden Niedrigenergieordnungen der Streuamplitude von vier Gluonen im heterotischen String auf Einschleifenniveau zu berechnen. Fur Stringamplituden auf Baumniveau bildet die Einwertigkeitsabbildung multipler Zetawerte offene Stringamplituden auf geschlossene Stringamplituden ab. Wir zeigen, dass ein bestimmter Vorschlag fur die Definition einer geeigneten einschleifen-Verallgemeinerung, der sogenannten elliptische Einwertigkeitsabbildung, nicht alle Terme im heterotischen String reproduzieren kann. Ferner studieren wir eine Erzeugendenfunktion, die vermutlich die Torusintegrale aller perturbativen Theorien geschlossener Strings enthalt. Wir bestimmen eine Differentialgleichung, die von dieser Erzeugendenfunktion erfullt wird und losen sie mit Hilfe von pfadgeordneten Exponentialen, was auf iterierte Integrale von holomorphen Eisensteinreihen fuhrt. Da eine ahnliche Konstruktion im offenen String zur Verfugung steht, eroffnet dies auserdem eine neue Perspektive auf die elliptische Einwertigkeitsabbildung.%%%%In this thesis, we investigate the low-energy expansion of scattering amplitudes of closed strings at one-loop level (i.e. at genus one) in a ten-dimensional Minkowski background using a special class of functions called modular graph forms. These allow for a systematic evaluation of the low-energy expansion and satisfy many non-trivial algebraic and differential relations. We study these relations in detail, leading to basis decompositions for a large number of modular graph forms which greatly reduce the complexity of the expansions of the integrals appearing in the amplitude. One of the results of this thesis is a Mathematica package which automatizes these simplifications. We use these techniques to compute the leading low-energy orders of the scattering amplitude of four gluons in the heterotic string at one-loop level. For tree-level string amplitudes, the single-valued map of multiple zeta values maps open-string amplitudes to closed-string amplitudes. The definition of a suitable one-loop generalization, a so-called elliptic single-valued map, is an active area of research and we show that a certain conjectural definition for this map, which was successfully applied to maximally supersymmetric amplitudes, cannot reproduce
在这次论文中，我们考察了关于集束膜片诱导的局部发展(也就是热那亚)，在米斯基十度背景中借助一组特定功能，也就是所谓的模块化格式化模式。这使得系统计算低层次演化并导致许多非显学代数和微分方程。研究这些数字背景资料，以及由此找到大量调制石墨烯的基本分解。这份论文的一个结果是数学包装，这只是个需要简化的算法。用这些技术来计算四子能见度的底层为Stringamplituden Baumniveau上形成Einwertigkeitsabbildung多重Zetawerte开放Stringamplituden语音闭合Stringamplituden .我们表明,某些建议给一个定义适当的einschleifen-Verallgemeinerung所谓椭圆Einwertigkeitsabbildung Terme的弦可以替代heterotischen .我们也研究一下方块函数。想到了所有的曲线理论的旋线功能。我们正在用方程式生成微分方程用细方程去除微分方程由于用一条隐藏的符咒设计出来了，它就会在椭圆信号图上开启新的视角。按原情况进行这一论点是为了全面评估低能源扩张和各种不同关系。“我们方程式之子”犹如研究创伤的方法有一个原因可以解释这种理论的数学造假。本计算的基础知识对弦放大器的弦值The定义of a的升值one-loop generalization, a so-called elliptic single-valued map, is active的苏格兰文化研究与人》我们节目的a certain conjectural定义for this map的计算什么successfully applied to maximally supersymmetric amplitudes, cannot reproduce所有条件在弦的heterotic有一套half-maximal ...
{"title":"Modular Graph Forms and Scattering Amplitudes in String Theory","authors":"Jan E. Gerken","doi":"10.18452/21829;","DOIUrl":"https://doi.org/10.18452/21829;","url":null,"abstract":"In dieser Dissertation untersuchen wir die Niedrigenergieentwicklung von Streuamplituden geschlossener Strings auf Einschleifenniveau (d.h. auf Genus eins) in einem zehndimensionalen Minkowski-Hintergrund mit Hilfe einer speziellen Klasse von Funktionen, den sogenannten modularen Graphenformen. Diese erlauben eine systematische Berechnung der Niedrigenergieentwicklung und erfullen viele nicht-triviale algebraische- und Differentialgleichungen. Wir studieren diese Relationen detailliert und leiten Basiszerlegungen fur eine grose Zahl modularer Graphenformen her. Eines der Ergebnisse dieser Dissertation ist ein Mathematica-Paket, welches diese Vereinfachungen automatisiert.\u0000\u0000Wir benutzen diese Techniken, um die fuhrenden Niedrigenergieordnungen der Streuamplitude von vier Gluonen im heterotischen String auf Einschleifenniveau zu berechnen.\u0000\u0000Fur Stringamplituden auf Baumniveau bildet die Einwertigkeitsabbildung multipler Zetawerte offene Stringamplituden auf geschlossene Stringamplituden ab. Wir zeigen, dass ein bestimmter Vorschlag fur die Definition einer geeigneten einschleifen-Verallgemeinerung, der sogenannten elliptische Einwertigkeitsabbildung, nicht alle Terme im heterotischen String reproduzieren kann.\u0000\u0000Ferner studieren wir eine Erzeugendenfunktion, die vermutlich die Torusintegrale aller perturbativen Theorien geschlossener Strings enthalt. Wir bestimmen eine Differentialgleichung, die von dieser Erzeugendenfunktion erfullt wird und losen sie mit Hilfe von pfadgeordneten Exponentialen, was auf iterierte Integrale von holomorphen Eisensteinreihen fuhrt. Da eine ahnliche Konstruktion im offenen String zur Verfugung steht, eroffnet dies auserdem eine neue Perspektive auf die elliptische Einwertigkeitsabbildung.%%%%In this thesis, we investigate the low-energy expansion of scattering amplitudes of closed strings at one-loop level (i.e. at genus one) in a ten-dimensional Minkowski background using a special class of functions called modular graph forms. These allow for a systematic evaluation of the low-energy expansion and satisfy many non-trivial algebraic and differential relations. We study these relations in detail, leading to basis decompositions for a large number of modular graph forms which greatly reduce the complexity of the expansions of the integrals appearing in the amplitude. One of the results of this thesis is a Mathematica package which automatizes these simplifications.\u0000\u0000We use these techniques to compute the leading low-energy orders of the scattering amplitude of four gluons in the heterotic string at one-loop level.\u0000\u0000For tree-level string amplitudes, the single-valued map of multiple zeta values maps open-string amplitudes to closed-string amplitudes. The definition of a suitable one-loop generalization, a so-called elliptic single-valued map, is an active area of research and we show that a certain conjectural definition for this map, which was successfully applied to maximally supersymmetric amplitudes, cannot reproduce ","PeriodicalId":8443,"journal":{"name":"arXiv: High Energy Physics - Theory","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89461385","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-09-03DOI: 10.1142/s0217732321500073
S. Ohya
Motivated by the Nahm's construction, in this paper we present a systematic construction of Schrodinger Hamiltonians for a spin-1/2 particle in which the Berry connection in the ground-state sector becomes the BPS monopole of $SU(2)$ Yang-Mills-Higgs theory. Our construction enjoys a single arbitrary monotonic function, thereby creating infinitely many quantum-mechanical models that simulate the BPS monopole in the space of model parameters.
{"title":"Models for the BPS Berry connection","authors":"S. Ohya","doi":"10.1142/s0217732321500073","DOIUrl":"https://doi.org/10.1142/s0217732321500073","url":null,"abstract":"Motivated by the Nahm's construction, in this paper we present a systematic construction of Schrodinger Hamiltonians for a spin-1/2 particle in which the Berry connection in the ground-state sector becomes the BPS monopole of $SU(2)$ Yang-Mills-Higgs theory. Our construction enjoys a single arbitrary monotonic function, thereby creating infinitely many quantum-mechanical models that simulate the BPS monopole in the space of model parameters.","PeriodicalId":8443,"journal":{"name":"arXiv: High Energy Physics - Theory","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88784198","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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