F. T. Brandt, J. Frenkel, S. Martins-Filho, D. G. C. McKeon
We examine the Einstein-Cartan (EC) theory in first-order form, which has a diffeomorphism as well as a local Lorentz invariance. We study the renormalizability of this theory in the framework of the Batalin-Vilkovisky formalism, which allows for a gauge invariant renormalization. Using the background field method, we discuss the gauge invariance of the background effective action and analyze the Ward identities which reflect the symmetries of the EC theory. As an application, we compute, in a general background gauge, the self-energy of the tetrad field at one-loop order.
{"title":"Renormalization of the Einstein-Cartan Theory in First-Order Form","authors":"F. T. Brandt, J. Frenkel, S. Martins-Filho, D. G. C. McKeon","doi":"arxiv-2409.10493","DOIUrl":"https://doi.org/arxiv-2409.10493","url":null,"abstract":"We examine the Einstein-Cartan (EC) theory in first-order form, which has a\u0000diffeomorphism as well as a local Lorentz invariance. We study the\u0000renormalizability of this theory in the framework of the Batalin-Vilkovisky\u0000formalism, which allows for a gauge invariant renormalization. Using the\u0000background field method, we discuss the gauge invariance of the background\u0000effective action and analyze the Ward identities which reflect the symmetries\u0000of the EC theory. As an application, we compute, in a general background gauge,\u0000the self-energy of the tetrad field at one-loop order.","PeriodicalId":501339,"journal":{"name":"arXiv - PHYS - High Energy Physics - Theory","volume":"38 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142251529","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}
R. Cartas-Fuentevilla, S. González-Salud, R. Bárcena-Ramos, J. Berra-Montiel
It is well known that the propagator for a massive scalar field is ill-defined in the coordinate space for $dgeq2$, in particular it diverges at the light-cone; we show that by using Lorentz symmetry breaking weighted measures, an infinite family of propagators can be constructed in an in-finite-simal strip near the light-cone, which are labeled by the weight of the measure; hence, the results will provide a finite quantum amplitude for a massive particle for propagating on the light-cone. The propagators regarded as smooth two-points functions, increase within a region smaller than the Compton wavelength, and decrease beyond that wavelength, and eventually drop off for large arguments. Although the time ordered propagators retain negative values regions for arbitrary values of the weight $s$ for the measures, the restriction $2
{"title":"The propagator field theory revisited: a Lorentz symmetry breaking approach","authors":"R. Cartas-Fuentevilla, S. González-Salud, R. Bárcena-Ramos, J. Berra-Montiel","doi":"arxiv-2409.10313","DOIUrl":"https://doi.org/arxiv-2409.10313","url":null,"abstract":"It is well known that the propagator for a massive scalar field is\u0000ill-defined in the coordinate space for $dgeq2$, in particular it diverges at\u0000the light-cone; we show that by using Lorentz symmetry breaking weighted\u0000measures, an infinite family of propagators can be constructed in an\u0000in-finite-simal strip near the light-cone, which are labeled by the weight of\u0000the measure; hence, the results will provide a finite quantum amplitude for a\u0000massive particle for propagating on the light-cone. The propagators regarded as\u0000smooth two-points functions, increase within a region smaller than the Compton\u0000wavelength, and decrease beyond that wavelength, and eventually drop off for\u0000large arguments. Although the time ordered propagators retain negative values\u0000regions for arbitrary values of the weight $s$ for the measures, the\u0000restriction $2<sleq d+1$ will guarantee the positivity for the amplitudes near\u0000the light cone.","PeriodicalId":501339,"journal":{"name":"arXiv - PHYS - High Energy Physics - Theory","volume":"54 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142251572","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 this work we investigate the phenomenological implications of several non-trivial axion-Higgs couplings, which cover most of the possible non-perturbative scenarios. Specifically we consider the combination of having higher order non-renormalizable Higgs-axion couplings originating from a weakly coupled effective theory combined with non-perturbative couplings of the form $sim epsilon Lambda_c^2|H|^2cos (frac{phi}{f_a})$. Since we consider the misalignment axion, the non-perturbative couplings can be expanded in the form of a perturbation expansion in powers of $phi/f_a$, thus after the electroweak symmetry breaking, the effective potential of the axion is drastically affected by these terms. We investigate the phenomenological implications of these terms for various values of the mass scale $Lambda_c$, and some scenarios are theoretically disfavored, while other scenarios with non-perturbative Higgs-axion couplings of the form $sim epsilon Lambda_c^2|H|^2cos (frac{phi}{f_a})$ with $Lambda_csim 10^{-10}times m_a$ and $m_asim 10^{-10},$eV, lead to a characteristic pattern in the stochastic gravitational wave background via the deformation of the background equation of state parameter occurring at frequencies probed by the Einstein Telescope. We also consider loop effects from the Higgs sector caused by the term $sim epsilon Lambda_c^2|H|^2cos (frac{phi}{f_a})$ if we close the Higgs in one loop.
{"title":"Theoretical Probes of Higgs-Axion non-perturbative Couplings","authors":"V. K. Oikonomou","doi":"arxiv-2409.10709","DOIUrl":"https://doi.org/arxiv-2409.10709","url":null,"abstract":"In this work we investigate the phenomenological implications of several\u0000non-trivial axion-Higgs couplings, which cover most of the possible\u0000non-perturbative scenarios. Specifically we consider the combination of having\u0000higher order non-renormalizable Higgs-axion couplings originating from a weakly\u0000coupled effective theory combined with non-perturbative couplings of the form\u0000$sim epsilon Lambda_c^2|H|^2cos (frac{phi}{f_a})$. Since we consider the\u0000misalignment axion, the non-perturbative couplings can be expanded in the form\u0000of a perturbation expansion in powers of $phi/f_a$, thus after the electroweak\u0000symmetry breaking, the effective potential of the axion is drastically affected\u0000by these terms. We investigate the phenomenological implications of these terms\u0000for various values of the mass scale $Lambda_c$, and some scenarios are\u0000theoretically disfavored, while other scenarios with non-perturbative\u0000Higgs-axion couplings of the form $sim epsilon Lambda_c^2|H|^2cos\u0000(frac{phi}{f_a})$ with $Lambda_csim 10^{-10}times m_a$ and $m_asim\u000010^{-10},$eV, lead to a characteristic pattern in the stochastic gravitational\u0000wave background via the deformation of the background equation of state\u0000parameter occurring at frequencies probed by the Einstein Telescope. We also\u0000consider loop effects from the Higgs sector caused by the term $sim epsilon\u0000Lambda_c^2|H|^2cos (frac{phi}{f_a})$ if we close the Higgs in one loop.","PeriodicalId":501339,"journal":{"name":"arXiv - PHYS - High Energy Physics - Theory","volume":"29 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142251524","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}
We propose a reinforcement learning-based search strategy to explore new physics beyond the Standard Model. The reinforcement learning, which is one of machine learning methods, is a powerful approach to find model parameters with phenomenological constraints. As a concrete example, we focus on a minimal axion model with a global $U(1)$ flavor symmetry. Agents of the learning succeed in finding $U(1)$ charge assignments of quarks and leptons solving the flavor and cosmological puzzles in the Standard Model, and find more than 150 realistic solutions for the quark sector taking renormalization effects into account. For the solutions found by the reinforcement learning-based analysis, we discuss the sensitivity of future experiments for the detection of an axion which is a Nambu-Goldstone boson of the spontaneously broken $U(1)$. We also examine how fast the reinforcement learning-based searching method finds the best discrete parameters in comparison with conventional optimization methods. In conclusion, the efficient parameter search based on the reinforcement learning-based strategy enables us to perform a statistical analysis of the vast parameter space associated with the axion model from flavor.
{"title":"Reinforcement learning-based statistical search strategy for an axion model from flavor","authors":"Satsuki Nishimura, Coh Miyao, Hajime Otsuka","doi":"arxiv-2409.10023","DOIUrl":"https://doi.org/arxiv-2409.10023","url":null,"abstract":"We propose a reinforcement learning-based search strategy to explore new\u0000physics beyond the Standard Model. The reinforcement learning, which is one of\u0000machine learning methods, is a powerful approach to find model parameters with\u0000phenomenological constraints. As a concrete example, we focus on a minimal\u0000axion model with a global $U(1)$ flavor symmetry. Agents of the learning\u0000succeed in finding $U(1)$ charge assignments of quarks and leptons solving the\u0000flavor and cosmological puzzles in the Standard Model, and find more than 150\u0000realistic solutions for the quark sector taking renormalization effects into\u0000account. For the solutions found by the reinforcement learning-based analysis,\u0000we discuss the sensitivity of future experiments for the detection of an axion\u0000which is a Nambu-Goldstone boson of the spontaneously broken $U(1)$. We also\u0000examine how fast the reinforcement learning-based searching method finds the\u0000best discrete parameters in comparison with conventional optimization methods.\u0000In conclusion, the efficient parameter search based on the reinforcement\u0000learning-based strategy enables us to perform a statistical analysis of the\u0000vast parameter space associated with the axion model from flavor.","PeriodicalId":501339,"journal":{"name":"arXiv - PHYS - High Energy Physics - Theory","volume":"2 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142251558","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}
We investigate the non-perturbative production of scalar particles within the Higgs-$R^2$ inflation model, focusing on a massive spectator field that interacts gravitationally via a non-minimal coupling to the Ricci scalar $R$. By transforming the model to the Einstein frame, where direct couplings between inflationary dynamics and the spectator field emerge, we analyze both perturbative and non-perturbative particle production. We solve the spectator field equation numerically, using the Bogolyubov transformation, to calculate the comoving particle density. Our findings indicate that particle production occurs for light particles with conformal coupling and for masses $m_chi > M/2$ in the minimally coupled scenario.
{"title":"Non-perturbative approach for scalar particle production in Higgs-$R^2$ inflation","authors":"Flavio Pineda, Luis O. Pimentel","doi":"arxiv-2409.09999","DOIUrl":"https://doi.org/arxiv-2409.09999","url":null,"abstract":"We investigate the non-perturbative production of scalar particles within the\u0000Higgs-$R^2$ inflation model, focusing on a massive spectator field that\u0000interacts gravitationally via a non-minimal coupling to the Ricci scalar $R$.\u0000By transforming the model to the Einstein frame, where direct couplings between\u0000inflationary dynamics and the spectator field emerge, we analyze both\u0000perturbative and non-perturbative particle production. We solve the spectator\u0000field equation numerically, using the Bogolyubov transformation, to calculate\u0000the comoving particle density. Our findings indicate that particle production\u0000occurs for light particles with conformal coupling and for masses $m_chi >\u0000M/2$ in the minimally coupled scenario.","PeriodicalId":501339,"journal":{"name":"arXiv - PHYS - High Energy Physics - Theory","volume":"14 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142251535","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}
Perseas Christodoulidis, Jinn-Ouk Gong, Wei-Chen Lin, Maria Mylova, Misao Sasaki
Chern-Simons gravity is known to suffer from graviton ghost production during inflation, which suppresses the parity-violating power spectrum at scales relevant to cosmic microwave background observations. In this work, we show that allowing the initial conditions of inflation to deviate from the standard Bunch-Davies state can enhance parity-violating non-Gaussianity in the scalar-tensor cross-bispectra. Our results reveal a significant additional contribution to the cross-bispectra in the flattened configuration, offering a new avenue to constrain parity-violating gravity.
{"title":"New shape for cross-bispectra in Chern-Simons gravity","authors":"Perseas Christodoulidis, Jinn-Ouk Gong, Wei-Chen Lin, Maria Mylova, Misao Sasaki","doi":"arxiv-2409.09935","DOIUrl":"https://doi.org/arxiv-2409.09935","url":null,"abstract":"Chern-Simons gravity is known to suffer from graviton ghost production during\u0000inflation, which suppresses the parity-violating power spectrum at scales\u0000relevant to cosmic microwave background observations. In this work, we show\u0000that allowing the initial conditions of inflation to deviate from the standard\u0000Bunch-Davies state can enhance parity-violating non-Gaussianity in the\u0000scalar-tensor cross-bispectra. Our results reveal a significant additional\u0000contribution to the cross-bispectra in the flattened configuration, offering a\u0000new avenue to constrain parity-violating gravity.","PeriodicalId":501339,"journal":{"name":"arXiv - PHYS - High Energy Physics - Theory","volume":"53 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142251678","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}
Thomas Gehrmann, Andreas von Manteuffel, Tong-Zhi Yang
Anomalous dimensions of twist-two operators govern the scale evolution of parton distribution functions. For off-shell external states, the physical twist-two operators mix with unknown gauge-variant operators under renormalization. In this talk, we apply the method proposed by us in~cite{Gehrmann:2023ksf} to compute all gauge-variant one-loop counterterm Feynman rules with five legs, which enter the determination of the four-loop splitting functions in QCD.
{"title":"Leading Twist-Two Gauge-Variant Counterterms","authors":"Thomas Gehrmann, Andreas von Manteuffel, Tong-Zhi Yang","doi":"arxiv-2409.10303","DOIUrl":"https://doi.org/arxiv-2409.10303","url":null,"abstract":"Anomalous dimensions of twist-two operators govern the scale evolution of\u0000parton distribution functions. For off-shell external states, the physical\u0000twist-two operators mix with unknown gauge-variant operators under\u0000renormalization. In this talk, we apply the method proposed by us\u0000in~cite{Gehrmann:2023ksf} to compute all gauge-variant one-loop counterterm\u0000Feynman rules with five legs, which enter the determination of the four-loop\u0000splitting functions in QCD.","PeriodicalId":501339,"journal":{"name":"arXiv - PHYS - High Energy Physics - Theory","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142251557","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}
Scattering calculations in curved spacetime are technically complicated and, in the case of a general spacetime metric, quite impossible. Even in the cases where perturbative scattering calculations can be done one has to be careful about what kind of particles are sensible to measure. Curved spacetime quantum field theories are then less conceptually clear than those in flat spacetime. In this article, we investigate an aspect of this conceptual confusion - the use of wave packets in defining the S-matrix. Wave packets are used in most standard textbook treatments to construct particle states and remove certain singularities in the definition of the S-matrix. We show that this method does not completely work in curved spacetimes first in a general way and then by way of a specific model. We also discuss related effects and suggest a method for doing curved spacetime scattering calculations. Our conclusion is that the most general method for scattering calculations in curved spacetimes requires the use of wave packets, which are typically absent in the literature.
弯曲时空中的散射计算在技术上是非常复杂的，而且在一般时空度量的情况下是完全不可能的。即使是在可以进行微扰散射计算的情况下，我们也必须小心谨慎地考虑什么样的粒子是可以测量的。在这篇文章中，我们将研究概念混淆的一个方面--在定义 S 矩阵时使用波包。在大多数标准教科书的论述中，波包被用来构造粒子态和消除 S 矩阵定义中的某些奇异性。我们首先以一般的方式，然后通过一个特定的模型，证明这种方法在弯曲时空中并不完全有效。我们还讨论了相关效应，并提出了一种进行弯曲时空散射计算的方法。我们的结论是，在弯曲时空中进行散射计算的最一般方法需要使用波包，而文献中通常没有波包。
{"title":"Packaging particles in curved spacetimes","authors":"Jesse Huhtala, Iiro Vilja","doi":"arxiv-2409.10133","DOIUrl":"https://doi.org/arxiv-2409.10133","url":null,"abstract":"Scattering calculations in curved spacetime are technically complicated and,\u0000in the case of a general spacetime metric, quite impossible. Even in the cases\u0000where perturbative scattering calculations can be done one has to be careful\u0000about what kind of particles are sensible to measure. Curved spacetime quantum\u0000field theories are then less conceptually clear than those in flat spacetime.\u0000In this article, we investigate an aspect of this conceptual confusion - the\u0000use of wave packets in defining the S-matrix. Wave packets are used in most\u0000standard textbook treatments to construct particle states and remove certain\u0000singularities in the definition of the S-matrix. We show that this method does\u0000not completely work in curved spacetimes first in a general way and then by way\u0000of a specific model. We also discuss related effects and suggest a method for\u0000doing curved spacetime scattering calculations. Our conclusion is that the most\u0000general method for scattering calculations in curved spacetimes requires the\u0000use of wave packets, which are typically absent in the literature.","PeriodicalId":501339,"journal":{"name":"arXiv - PHYS - High Energy Physics - Theory","volume":"3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142251669","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}
Quantum field theories with quenched disorder are so hard to study that even exactly solvable free theories present puzzling aspects. We consider a free scalar field $phi$ in $d$ dimensions coupled to a random source $h$ with quenched disorder. Despite the presence of a mass scale governing the disorder distribution, we derive a new description of the theory that allows us to show that the theory is gapless and invariant under conformal symmetry, which acts in a non-trivial way on $phi$ and $h$. This manifest CFT description reveals the presence of exotic continuous symmetries, such as nilpotent bosonic ones, in the quenched theory. We also reconsider Cardy's CFT description defined through the replica trick. In this description, the nilpotent symmetries reveal a striking resemblance with Parisi-Sourlas supersymmetries. We provide explicit maps of correlation functions between such CFTs and the original quenched theory. The maps are non-trivial and show that conformal behaviour is manifest only when considering suitable linear combinations of averages of products of correlators. We also briefly discuss how familiar notions like normal ordering of composite operators and OPE can be generalized in the presence of the more complicated local observables in the quenched theory.
{"title":"The random free field scalar theory","authors":"Alessandro Piazza, Marco Serone, Emilio Trevisani","doi":"arxiv-2409.10608","DOIUrl":"https://doi.org/arxiv-2409.10608","url":null,"abstract":"Quantum field theories with quenched disorder are so hard to study that even\u0000exactly solvable free theories present puzzling aspects. We consider a free\u0000scalar field $phi$ in $d$ dimensions coupled to a random source $h$ with\u0000quenched disorder. Despite the presence of a mass scale governing the disorder\u0000distribution, we derive a new description of the theory that allows us to show\u0000that the theory is gapless and invariant under conformal symmetry, which acts\u0000in a non-trivial way on $phi$ and $h$. This manifest CFT description reveals\u0000the presence of exotic continuous symmetries, such as nilpotent bosonic ones,\u0000in the quenched theory. We also reconsider Cardy's CFT description defined\u0000through the replica trick. In this description, the nilpotent symmetries reveal\u0000a striking resemblance with Parisi-Sourlas supersymmetries. We provide explicit\u0000maps of correlation functions between such CFTs and the original quenched\u0000theory. The maps are non-trivial and show that conformal behaviour is manifest\u0000only when considering suitable linear combinations of averages of products of\u0000correlators. We also briefly discuss how familiar notions like normal ordering\u0000of composite operators and OPE can be generalized in the presence of the more\u0000complicated local observables in the quenched theory.","PeriodicalId":501339,"journal":{"name":"arXiv - PHYS - High Energy Physics - Theory","volume":"38 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142251516","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}
String scattering amplitudes in the high energy asymptotic region have been studied by saddle point approximation. Recently, it was pointed out that infinitely many complex saddles contribute to string amplitudes even at tree-level after redefining the original formal integration contour so that the new contour analytically continues amplitudes appropriately. It is a challenging problem to identify which saddles contribute to higher genus corrections of string amplitudes. In this paper, we construct QFT toy models which have the same infinite mass tower as string amplitudes but ignoring degeneracies. Their higher loop Feynman diagrams are evaluated by identifying their contributing complex saddles. We find that the saddles associated with infinitely many stringy excitations provide highly oscillatory terms to the amplitudes. We conjecture that string amplitudes, as functions of momenta, approach multi-fractal functions in the high energy asymptotic regions if higher genus contributions are fully included. Their fractal dimensions should be determined purely by the type of string theory and the spacetime dimension where string scatterings occur.
{"title":"Complex Saddles of Truncated String Amplitudes","authors":"Takuya Yoda","doi":"arxiv-2409.10241","DOIUrl":"https://doi.org/arxiv-2409.10241","url":null,"abstract":"String scattering amplitudes in the high energy asymptotic region have been\u0000studied by saddle point approximation. Recently, it was pointed out that\u0000infinitely many complex saddles contribute to string amplitudes even at\u0000tree-level after redefining the original formal integration contour so that the\u0000new contour analytically continues amplitudes appropriately. It is a\u0000challenging problem to identify which saddles contribute to higher genus\u0000corrections of string amplitudes. In this paper, we construct QFT toy models\u0000which have the same infinite mass tower as string amplitudes but ignoring\u0000degeneracies. Their higher loop Feynman diagrams are evaluated by identifying\u0000their contributing complex saddles. We find that the saddles associated with\u0000infinitely many stringy excitations provide highly oscillatory terms to the\u0000amplitudes. We conjecture that string amplitudes, as functions of momenta,\u0000approach multi-fractal functions in the high energy asymptotic regions if\u0000higher genus contributions are fully included. Their fractal dimensions should\u0000be determined purely by the type of string theory and the spacetime dimension\u0000where string scatterings occur.","PeriodicalId":501339,"journal":{"name":"arXiv - PHYS - High Energy Physics - Theory","volume":"29 22 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142251530","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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