Pub Date : 2019-09-13DOI: 10.4310/ATMP.2021.v25.n1.a5
Ján Pulmann, Pavol vSevera, F. Valach
We consider a TFT on the product of a manifold with an interval, together with a topological and a non-topological boundary condition imposed at the two respective ends. The resulting (in general higher gauge) field theory is non-topological, with different choices of the topological conditions leading to field theories dual to each other. In particular, we recover the electric-magnetic duality, the Poisson-Lie T-duality, and we obtain new higher analogues thereof.
{"title":"A nonabelian duality for (higher) gauge theories","authors":"Ján Pulmann, Pavol vSevera, F. Valach","doi":"10.4310/ATMP.2021.v25.n1.a5","DOIUrl":"https://doi.org/10.4310/ATMP.2021.v25.n1.a5","url":null,"abstract":"We consider a TFT on the product of a manifold with an interval, together with a topological and a non-topological boundary condition imposed at the two respective ends. The resulting (in general higher gauge) field theory is non-topological, with different choices of the topological conditions leading to field theories dual to each other. In particular, we recover the electric-magnetic duality, the Poisson-Lie T-duality, and we obtain new higher analogues thereof.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":"55 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2019-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88469399","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-09-09DOI: 10.4310/ATMP.2021.v25.n1.a1
M. Ashwinkumar, Kee-Seng Png, M. Tan
Generalizing our ideas in [arXiv:1006.3313], we explain how topologically-twisted N = 2 gauge theory on a four-manifold with boundary, will allow us to furnish purely physical proofs of (i) the Atiyah-Floer conjecture, (ii) Mu˜noz’s theorem relating quantum and instanton Floer cohomology, (iii) their monopole counterparts, and (iv) their higher rank generalizations. In the case where the boundary is a Seifert manifold, one can also relate its instanton Floer homology to modules of an affine algebra via a 2d A-model with target the based loop group. As an offshoot, we will be able to demonstrate an action of the affine algebra on the quantum cohomology of the moduli space of flat connections on a Riemann surface, as well as derive the Verlinde formula.
{"title":"Boundary $mathcal{N} = 2$ theory, Floer homologies, affine algebras, and the Verlinde formula","authors":"M. Ashwinkumar, Kee-Seng Png, M. Tan","doi":"10.4310/ATMP.2021.v25.n1.a1","DOIUrl":"https://doi.org/10.4310/ATMP.2021.v25.n1.a1","url":null,"abstract":"Generalizing our ideas in [arXiv:1006.3313], we explain how topologically-twisted N = 2 gauge theory on a four-manifold with boundary, will allow us to furnish purely physical proofs of (i) the Atiyah-Floer conjecture, (ii) Mu˜noz’s theorem relating quantum and instanton Floer cohomology, (iii) their monopole counterparts, and (iv) their higher rank generalizations. In the case where the boundary is a Seifert manifold, one can also relate its instanton Floer homology to modules of an affine algebra via a 2d A-model with target the based loop group. As an offshoot, we will be able to demonstrate an action of the affine algebra on the quantum cohomology of the moduli space of flat connections on a Riemann surface, as well as derive the Verlinde formula.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":"7 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2019-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90410968","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-08-16DOI: 10.4310/ATMP.2021.v25.n6.a4
W. Gu, J. Guo, E. Sharpe
In this paper we give a proposal for mirrors to (0,2) supersymmetric gauged linear sigma models (GLSMs), for those (0,2) GLSMs which are deformations of (2,2) GLSMs. Specifically, we propose a construction of (0,2) mirrors for (0,2) GLSMs with E terms that are linear and diagonal, reducing to both the Hori-Vafa prescription as well as a recent (2,2) nonabelian mirrors proposal on the (2,2) locus. For the special case of abelian (0,2) GLSMs, two fo the authors have previously proposed a systematic construction, which is both simplified and generalized by the proposal here.
{"title":"A proposal for nonabelian $(0,2)$ mirrors","authors":"W. Gu, J. Guo, E. Sharpe","doi":"10.4310/ATMP.2021.v25.n6.a4","DOIUrl":"https://doi.org/10.4310/ATMP.2021.v25.n6.a4","url":null,"abstract":"In this paper we give a proposal for mirrors to (0,2) supersymmetric gauged linear sigma models (GLSMs), for those (0,2) GLSMs which are deformations of (2,2) GLSMs. Specifically, we propose a construction of (0,2) mirrors for (0,2) GLSMs with E terms that are linear and diagonal, reducing to both the Hori-Vafa prescription as well as a recent (2,2) nonabelian mirrors proposal on the (2,2) locus. For the special case of abelian (0,2) GLSMs, two fo the authors have previously proposed a systematic construction, which is both simplified and generalized by the proposal here.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":"46 5 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2019-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77308536","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-07-29DOI: 10.4310/atmp.2021.v25.n2.a2
E. Babichev, K. Izumi, Norihiro Tanahashi, Masahide Yamaguchi
We formulate explicitly the necessary and sufficient conditions for the local invertibility of a field transformation involving derivative terms. Our approach is to apply the method of characteristics of differential equations, by treating such a transformation as differential equations that give new variables in terms of original ones. The obtained results generalise the well-known and widely used inverse function theorem. Taking into account that field transformations are ubiquitous in modern physics and mathematics, our criteria for invertibility will find many useful applications.
{"title":"Invertible field transformations with derivatives: necessary and sufficient conditions","authors":"E. Babichev, K. Izumi, Norihiro Tanahashi, Masahide Yamaguchi","doi":"10.4310/atmp.2021.v25.n2.a2","DOIUrl":"https://doi.org/10.4310/atmp.2021.v25.n2.a2","url":null,"abstract":"We formulate explicitly the necessary and sufficient conditions for the local invertibility of a field transformation involving derivative terms. Our approach is to apply the method of characteristics of differential equations, by treating such a transformation as differential equations that give new variables in terms of original ones. The obtained results generalise the well-known and widely used inverse function theorem. Taking into account that field transformations are ubiquitous in modern physics and mathematics, our criteria for invertibility will find many useful applications.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":"11 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2019-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86721338","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-07-19DOI: 10.4310/ATMP.2021.v25.n6.a2
J. Franccois
We propose a generalisation of the notion of associated bundles to a principal bundle constructed via group action cocycles rather than via mere representations of the structure group. We devise a notion of connection generalising Ehresmann connection on principal bundles, giving rise to the appropriate covariant derivative on sections of these twisted associated bundles (and on twisted tensorial forms). We study the action of the group of vertical automorphisms on the objects introduced (active gauge transformations). We also provide the gluing properties of the local representatives (passive gauge transformations). The latter are generalised gauge fields: They satisfy the gauge principle of physics, but are of a different geometric nature than standard Yang-Mills fields. We also examine the conditions under which this new geometry coexists and mixes with the standard one. We show that (standard) conformal tractors and Penrose's twistors can be seen as simple instances of this general picture. We also indicate that the twisted geometry arises naturally in the definition and study of anomalies in quantum gauge field theory.
{"title":"Twisted gauge fields","authors":"J. Franccois","doi":"10.4310/ATMP.2021.v25.n6.a2","DOIUrl":"https://doi.org/10.4310/ATMP.2021.v25.n6.a2","url":null,"abstract":"We propose a generalisation of the notion of associated bundles to a principal bundle constructed via group action cocycles rather than via mere representations of the structure group. We devise a notion of connection generalising Ehresmann connection on principal bundles, giving rise to the appropriate covariant derivative on sections of these twisted associated bundles (and on twisted tensorial forms). We study the action of the group of vertical automorphisms on the objects introduced (active gauge transformations). We also provide the gluing properties of the local representatives (passive gauge transformations). The latter are generalised gauge fields: They satisfy the gauge principle of physics, but are of a different geometric nature than standard Yang-Mills fields. We also examine the conditions under which this new geometry coexists and mixes with the standard one. We show that (standard) conformal tractors and Penrose's twistors can be seen as simple instances of this general picture. We also indicate that the twisted geometry arises naturally in the definition and study of anomalies in quantum gauge field theory.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":"14 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2019-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74470280","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-07-10DOI: 10.4310/ATMP.2020.v24.n4.a1
R. C. Avohou, J. B. Geloun, N. Dub
$O(N)$ invariants are the observables of real tensor models. We use regular colored graphs to represent these invariants, the valence of the vertices of the graphs relates to the tensor rank. We enumerate $O(N)$ invariants as $d$-regular graphs, using permutation group techniques. We also list their generating functions and give (software) algorithms computing their number at an arbitrary rank and an arbitrary number of vertices. As an interesting property, we reveal that the algebraic structure which organizes these invariants differs from that of the unitary invariants. The underlying topological field theory formulation of the rank $d$ counting shows that it corresponds to counting of coverings of the $d-1$ cylinders sharing the same boundary circle and with $d$ defects. At fixed rank and fixed number of vertices, an associative semi-simple algebra with dimension the number of invariants naturally emerges from the formulation. Using the representation theory of the symmetric group, we enlighten a few crucial facts: the enumeration of $O(N)$ invariants gives a sum of constrained Kronecker coefficients; there is a representation theoretic orthogonal base of the algebra that reflects its dimension; normal ordered 2-pt correlators of the Gaussian models evaluate using permutation group language, and further, via representation theory, these functions provide other representation theoretic orthogonal bases of the algebra.
{"title":"On the counting of $O(N)$ tensor invariants","authors":"R. C. Avohou, J. B. Geloun, N. Dub","doi":"10.4310/ATMP.2020.v24.n4.a1","DOIUrl":"https://doi.org/10.4310/ATMP.2020.v24.n4.a1","url":null,"abstract":"$O(N)$ invariants are the observables of real tensor models. We use regular colored graphs to represent these invariants, the valence of the vertices of the graphs relates to the tensor rank. We enumerate $O(N)$ invariants as $d$-regular graphs, using permutation group techniques. We also list their generating functions and give (software) algorithms computing their number at an arbitrary rank and an arbitrary number of vertices. As an interesting property, we reveal that the algebraic structure which organizes these invariants differs from that of the unitary invariants. The underlying topological field theory formulation of the rank $d$ counting shows that it corresponds to counting of coverings of the $d-1$ cylinders sharing the same boundary circle and with $d$ defects. At fixed rank and fixed number of vertices, an associative semi-simple algebra with dimension the number of invariants naturally emerges from the formulation. Using the representation theory of the symmetric group, we enlighten a few crucial facts: the enumeration of $O(N)$ invariants gives a sum of constrained Kronecker coefficients; there is a representation theoretic orthogonal base of the algebra that reflects its dimension; normal ordered 2-pt correlators of the Gaussian models evaluate using permutation group language, and further, via representation theory, these functions provide other representation theoretic orthogonal bases of the algebra.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":"26 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2019-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80277111","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-07-07DOI: 10.4310/atmp.2020.v24.n6.a4
D. Stanford, E. Witten
We generalize the recently discovered relationship between JT gravity and double-scaled random matrix theory to the case that the boundary theory may have time-reversal symmetry and may have fermions with or without supersymmetry. The matching between variants of JT gravity and matrix ensembles depends on the assumed symmetries. Time-reversal symmetry in the boundary theory means that unorientable spacetimes must be considered in the bulk. In such a case, the partition function of JT gravity is still related to the volume of the moduli space of conformal structures, but this volume has a quantum correction and has to be computed using Reidemeister-Ray-Singer "torsion." Presence of fermions in the boundary theory (and thus a symmetry $(-1)^F$) means that the bulk has a spin or pin structure. Supersymmetry in the boundary means that the bulk theory is associated to JT supergravity and is related to the volume of the moduli space of super Riemann surfaces rather than of ordinary Riemann surfaces. In all cases we match JT gravity or supergravity with an appropriate random matrix ensemble. All ten standard random matrix ensembles make an appearance -- the three Dyson ensembles and the seven Altland-Zirnbauer ensembles. To facilitate the analysis, we extend to the other ensembles techniques that are most familiar in the case of the original Wigner-Dyson ensemble of hermitian matrices. We also generalize Mirzakhani's recursion for the volumes of ordinary moduli space to the case of super Riemann surfaces.
{"title":"JT gravity and the ensembles of random matrix theory","authors":"D. Stanford, E. Witten","doi":"10.4310/atmp.2020.v24.n6.a4","DOIUrl":"https://doi.org/10.4310/atmp.2020.v24.n6.a4","url":null,"abstract":"We generalize the recently discovered relationship between JT gravity and double-scaled random matrix theory to the case that the boundary theory may have time-reversal symmetry and may have fermions with or without supersymmetry. The matching between variants of JT gravity and matrix ensembles depends on the assumed symmetries. Time-reversal symmetry in the boundary theory means that unorientable spacetimes must be considered in the bulk. In such a case, the partition function of JT gravity is still related to the volume of the moduli space of conformal structures, but this volume has a quantum correction and has to be computed using Reidemeister-Ray-Singer \"torsion.\" Presence of fermions in the boundary theory (and thus a symmetry $(-1)^F$) means that the bulk has a spin or pin structure. Supersymmetry in the boundary means that the bulk theory is associated to JT supergravity and is related to the volume of the moduli space of super Riemann surfaces rather than of ordinary Riemann surfaces. In all cases we match JT gravity or supergravity with an appropriate random matrix ensemble. All ten standard random matrix ensembles make an appearance -- the three Dyson ensembles and the seven Altland-Zirnbauer ensembles. To facilitate the analysis, we extend to the other ensembles techniques that are most familiar in the case of the original Wigner-Dyson ensemble of hermitian matrices. We also generalize Mirzakhani's recursion for the volumes of ordinary moduli space to the case of super Riemann surfaces.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":"81 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2019-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88284595","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-06-23DOI: 10.4310/ATMP.2022.v26.n5.a8
Cid Reyes-Bustos, M. Wakayama
The quantum Rabi model (QRM) is widely recognized as a particularly important model in quantum optics. It is considered to be the simplest and most fundamental system describing quantum light-matter interaction. The objective of the paper is to give an analytical formula of the heat kernel of the Hamiltonian explicitly by infinite series of iterated integrals. The derivation of the formula is based on the direct evaluation of the Trotter-Kato product formula without the use of Feynman-Kac path integrals. More precisely, the infinite sum in the expression of the heat kernel arises from the reduction of the Trotter-Kato product formula into sums over the orbits of the action of the infinite symmetric group $mathfrak{S}_infty$ on the group $mathbb{Z}_2^{infty}$, and the iterated integrals are then considered as the orbital integral for each orbit. Here, the groups $ mathbb{Z}_2^{infty} $ and $mathfrak{S}_infty$ are the inductive limit of the families ${mathbb{Z}_2^n}_{ngeq0}$ and ${mathfrak{S}_n}_{ngeq0}$, respectively. In order to complete the reduction, an extensive study of harmonic (Fourier) analysis on the inductive family of abelian groups $mathbb{Z}_2^n, (n geq0)$ together with a graph theoretical investigation is crucial. To the best knowledge of the authors, this is the first explicit computation for obtaining a closed formula of the heat kernel for a non-trivial realistic interacting quantum system. The heat kernel of this model is further given by a two-by-two matrix valued function and is expressed as a direct sum of two respective heat kernels representing the parity ($mathbb{Z}_2$-symmetry) decomposition of the Hamiltonian by parity.
{"title":"Heat kernel for the quantum Rabi model","authors":"Cid Reyes-Bustos, M. Wakayama","doi":"10.4310/ATMP.2022.v26.n5.a8","DOIUrl":"https://doi.org/10.4310/ATMP.2022.v26.n5.a8","url":null,"abstract":"The quantum Rabi model (QRM) is widely recognized as a particularly important model in quantum optics. It is considered to be the simplest and most fundamental system describing quantum light-matter interaction. The objective of the paper is to give an analytical formula of the heat kernel of the Hamiltonian explicitly by infinite series of iterated integrals. The derivation of the formula is based on the direct evaluation of the Trotter-Kato product formula without the use of Feynman-Kac path integrals. More precisely, the infinite sum in the expression of the heat kernel arises from the reduction of the Trotter-Kato product formula into sums over the orbits of the action of the infinite symmetric group $mathfrak{S}_infty$ on the group $mathbb{Z}_2^{infty}$, and the iterated integrals are then considered as the orbital integral for each orbit. Here, the groups $ mathbb{Z}_2^{infty} $ and $mathfrak{S}_infty$ are the inductive limit of the families ${mathbb{Z}_2^n}_{ngeq0}$ and ${mathfrak{S}_n}_{ngeq0}$, respectively. In order to complete the reduction, an extensive study of harmonic (Fourier) analysis on the inductive family of abelian groups $mathbb{Z}_2^n, (n geq0)$ together with a graph theoretical investigation is crucial. To the best knowledge of the authors, this is the first explicit computation for obtaining a closed formula of the heat kernel for a non-trivial realistic interacting quantum system. The heat kernel of this model is further given by a two-by-two matrix valued function and is expressed as a direct sum of two respective heat kernels representing the parity ($mathbb{Z}_2$-symmetry) decomposition of the Hamiltonian by parity.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":"28 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2019-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74792004","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We prove that the blowup term of a blowup solution of Jang's equation on an initial data set (M,g,k) near an arbitrary strictly stable MOTS $ Sigma $ is exactly $ -frac{1}{sqrt{lambda}}log tau $, where $ tau $ is the distance from $ Sigma $ and $ lambda $ is the principal eigenvalue of the MOTS stability operator of $ Sigma $. We also prove that the gradient of the solution is of order $ tau^{-1} $. Moreover, we apply these results to get a Penrose-like inequality under additional assumptions.
证明了在任意严格稳定MOTS $ Sigma $附近的初始数据集(M,g,k)上Jang方程的爆破解的爆破项恰好为$ -frac{1}{sqrt{lambda}}log tau $，其中$ tau $为到$ Sigma $的距离，$ lambda $为$ Sigma $的MOTS稳定性算子的主特征值。我们还证明了解的梯度为$ tau^{-1} $阶。此外，我们将这些结果应用于在附加假设下的类penrose不等式。
{"title":"Blowup rate control for solution of Jang’s equation and its application to Penrose inequality","authors":"Wenhuan Yu","doi":"10.7916/d8-avnq-g588","DOIUrl":"https://doi.org/10.7916/d8-avnq-g588","url":null,"abstract":"We prove that the blowup term of a blowup solution of Jang's equation on an initial data set (M,g,k) near an arbitrary strictly stable MOTS $ Sigma $ is exactly $ -frac{1}{sqrt{lambda}}log tau $, where $ tau $ is the distance from $ Sigma $ and $ lambda $ is the principal eigenvalue of the MOTS stability operator of $ Sigma $. We also prove that the gradient of the solution is of order $ tau^{-1} $. Moreover, we apply these results to get a Penrose-like inequality under additional assumptions.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":"31 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2019-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79056127","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-06-17DOI: 10.4310/atmp.2021.v25.n5.a2
H. Clemens, S. Raby
Finding the $F$-theory dual of a Heterotic model with Wilson-line symmetry breaking presents the challenge of achieving the dual $mathbb{Z}_{2}$-action on the $F$-theory model in such a way that the $mathbb{Z}_{2}$-quotient is Calabi-Yau with an Enriques $mathrm{GUT}$ surface over which $SUleft(5right)_{gauge}$ symmetry is maintained. We propose a new way to approach this problem by taking advantage of a little-noticed choice in the application of Narasimhan-Seshadri equivalence between real $E_{8}$-bundles with Yang-Mills connection and their associated complex holomorphic $E_{8}^{mathbb{C}}$-bundles, namely the one given by the real outer automorphism of $E_{8}^{mathbb{C}}$ by complex conjugation. The triviality of the restriction on the compact real form $E_{8}$ allows one to introduce it into the $mathbb{Z}_{2}$-action, thereby restoring $E_{8}$- and hence $SUleft(5right)_{gauge}$ -symmetry on which the Wilson line can be wrapped.
{"title":"Heterotic/$F$-theory duality and Narasimhan–Seshadri equivalence","authors":"H. Clemens, S. Raby","doi":"10.4310/atmp.2021.v25.n5.a2","DOIUrl":"https://doi.org/10.4310/atmp.2021.v25.n5.a2","url":null,"abstract":"Finding the $F$-theory dual of a Heterotic model with Wilson-line symmetry breaking presents the challenge of achieving the dual $mathbb{Z}_{2}$-action on the $F$-theory model in such a way that the $mathbb{Z}_{2}$-quotient is Calabi-Yau with an Enriques $mathrm{GUT}$ surface over which $SUleft(5right)_{gauge}$ symmetry is maintained. We propose a new way to approach this problem by taking advantage of a little-noticed choice in the application of Narasimhan-Seshadri equivalence between real $E_{8}$-bundles with Yang-Mills connection and their associated complex holomorphic $E_{8}^{mathbb{C}}$-bundles, namely the one given by the real outer automorphism of $E_{8}^{mathbb{C}}$ by complex conjugation. The triviality of the restriction on the compact real form $E_{8}$ allows one to introduce it into the $mathbb{Z}_{2}$-action, thereby restoring $E_{8}$- and hence $SUleft(5right)_{gauge}$ -symmetry on which the Wilson line can be wrapped.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":"67 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2019-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90401372","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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