Pub Date : 2023-01-01DOI: 10.4310/atmp.2023.v27.n2.a1
Kiyonori Gomi, Mayuko Yamashita
{"title":"Differential $KO$-theory via gradations and mass terms","authors":"Kiyonori Gomi, Mayuko Yamashita","doi":"10.4310/atmp.2023.v27.n2.a1","DOIUrl":"https://doi.org/10.4310/atmp.2023.v27.n2.a1","url":null,"abstract":"","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":"130 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136303536","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 : 2023-01-01DOI: 10.4310/atmp.2023.v27.n1.a2
M. Taylor
{"title":"$T bar{T}$ deformations in general dimensions","authors":"M. Taylor","doi":"10.4310/atmp.2023.v27.n1.a2","DOIUrl":"https://doi.org/10.4310/atmp.2023.v27.n1.a2","url":null,"abstract":"","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":"2 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87345130","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 : 2023-01-01DOI: 10.4310/atmp.2023.v27.n2.a3
Sergei Gukov, Artan Sheshmani, Shing-Tung Yau
{"title":"$3$-manifolds and Vafa–Witten theory","authors":"Sergei Gukov, Artan Sheshmani, Shing-Tung Yau","doi":"10.4310/atmp.2023.v27.n2.a3","DOIUrl":"https://doi.org/10.4310/atmp.2023.v27.n2.a3","url":null,"abstract":"","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":"2012 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136302861","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 : 2023-01-01DOI: 10.4310/atmp.2023.v27.n2.a2
Tom Banks, Patrick Draper, Bingnan Zhang
We argue that two-dimensional dilaton gravity models can all be derived from an analog of Jacobson's covariant version of the first law of thermodynamics. We then specialize to the JT gravity model and couple it to massless fermions. This model is exactly soluble in quantum field theory, and we present a new derivation of that result. The field theory model violates two principles one might want to impose on a quantum theory of gravity describing the near horizon region of an extremal charged black hole in four dimensions: finiteness of the entropy for finite causal diamonds, and the absence of global conservation laws. It preserves an infinite number of conservation laws that one would have expected to be violated, since the fermion state on each side of the $AdS_2$ wormhole is unavoidably thermal. We describe a cutoff version of the model, with extra interactions, which cures these difficulties. Our UV completion of the model depends on the AKK map of non-relativistic fermions in an inverted oscillator potential to Weyl fermions in Minkowski space. We argue that gauging the $Z_2$ symmetry of the oscillator model, using a density matrix with temperature that depends on the oscillator coordinates, and inserting chaotic interactions at (almost) infinite oscillator coordinate, we obtain a model with properties expected of quantum gravity in the near horizon region of an extremal charged black hole in four dimensions.
{"title":"JT gravity coupled to fermions","authors":"Tom Banks, Patrick Draper, Bingnan Zhang","doi":"10.4310/atmp.2023.v27.n2.a2","DOIUrl":"https://doi.org/10.4310/atmp.2023.v27.n2.a2","url":null,"abstract":"We argue that two-dimensional dilaton gravity models can all be derived from an analog of Jacobson's covariant version of the first law of thermodynamics. We then specialize to the JT gravity model and couple it to massless fermions. This model is exactly soluble in quantum field theory, and we present a new derivation of that result. The field theory model violates two principles one might want to impose on a quantum theory of gravity describing the near horizon region of an extremal charged black hole in four dimensions: finiteness of the entropy for finite causal diamonds, and the absence of global conservation laws. It preserves an infinite number of conservation laws that one would have expected to be violated, since the fermion state on each side of the $AdS_2$ wormhole is unavoidably thermal. We describe a cutoff version of the model, with extra interactions, which cures these difficulties. Our UV completion of the model depends on the AKK map of non-relativistic fermions in an inverted oscillator potential to Weyl fermions in Minkowski space. We argue that gauging the $Z_2$ symmetry of the oscillator model, using a density matrix with temperature that depends on the oscillator coordinates, and inserting chaotic interactions at (almost) infinite oscillator coordinate, we obtain a model with properties expected of quantum gravity in the near horizon region of an extremal charged black hole in four dimensions.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136303537","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 : 2023-01-01DOI: 10.4310/atmp.2023.v27.n2.a4
Tamer Tlas
{"title":"Yang–Mills as a constrained Gaussian","authors":"Tamer Tlas","doi":"10.4310/atmp.2023.v27.n2.a4","DOIUrl":"https://doi.org/10.4310/atmp.2023.v27.n2.a4","url":null,"abstract":"","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136303568","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 : 2022-12-27DOI: 10.4310/atmp.2022.v26.n2.a3
Herbert Clemens, Stuart Raby
In a previous paper, the authors showed the advantages of building a $mathbb{Z}_2$-action into an $F$-theory model $W_4 / B_3$, namely the action of complex conjugation on the complex algebraic group with compact real form $E_8$. The goal of this paper is to construct the Fano threefold $B_3$ directly from the roots of $SU(5)$ in such a way that the action of complex conjugation is exactly the desired $mathbb{Z}_2$-action and the quotient of this action on $W_4 / B_3$ and its Heterotic dual have the phenomenologically correct invariants.
{"title":"$F$-theory over a Fano threefold built from $A_4$-roots","authors":"Herbert Clemens, Stuart Raby","doi":"10.4310/atmp.2022.v26.n2.a3","DOIUrl":"https://doi.org/10.4310/atmp.2022.v26.n2.a3","url":null,"abstract":"In a previous paper, the authors showed the advantages of building a $mathbb{Z}_2$-action into an $F$-theory model $W_4 / B_3$, namely the action of complex conjugation on the complex algebraic group with compact real form $E_8$. The goal of this paper is to construct the Fano threefold $B_3$ directly from the roots of $SU(5)$ in such a way that the action of complex conjugation is exactly the desired $mathbb{Z}_2$-action and the quotient of this action on $W_4 / B_3$ and its Heterotic dual have the phenomenologically correct invariants.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":"1 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138527192","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 : 2022-12-16DOI: 10.4310/atmp.2023.v27.n1.a6
E. Witten
We describe a simple gauge-fixing that leads to a construction of a quantum Hilbert space for quantum gravity in an asymptotically Anti de Sitter spacetime, valid to all orders of perturbation theory. The construction is motivated by a relationship of the phase space of gravity in asymptotically Anti de Sitter spacetime to a cotangent bundle. We describe what is known about this relationship and some extensions that might plausibly be true. A key fact is that, under certain conditions, the Einstein Hamiltonian constraint equation can be viewed as a way to gauge fix the group of conformal rescalings of the metric of a Cauchy hypersurface. An analog of the procedure that we follow for Anti de Sitter gravity leads to standard results for a Klein-Gordon particle.
{"title":"A note on the canonical formalism for gravity","authors":"E. Witten","doi":"10.4310/atmp.2023.v27.n1.a6","DOIUrl":"https://doi.org/10.4310/atmp.2023.v27.n1.a6","url":null,"abstract":"We describe a simple gauge-fixing that leads to a construction of a quantum Hilbert space for quantum gravity in an asymptotically Anti de Sitter spacetime, valid to all orders of perturbation theory. The construction is motivated by a relationship of the phase space of gravity in asymptotically Anti de Sitter spacetime to a cotangent bundle. We describe what is known about this relationship and some extensions that might plausibly be true. A key fact is that, under certain conditions, the Einstein Hamiltonian constraint equation can be viewed as a way to gauge fix the group of conformal rescalings of the metric of a Cauchy hypersurface. An analog of the procedure that we follow for Anti de Sitter gravity leads to standard results for a Klein-Gordon particle.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":"113 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85493837","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 : 2022-10-13DOI: 10.4310/atmp.2023.v27.n1.a5
Umang Mehta, Shiraz Minwalla, Chintan Patel, S. Prakash, Kartik Sharma
We present a conjecture for the crossing symmetry rules for Chern-Simons gauge theories interacting with massive matter in $2+1$ dimensions. Our crossing rules are given in terms of the expectation values of particular tangles of Wilson lines, and reduce to the standard rules at large Chern-Simons level. We present completely explicit results for the special case of two fundamental and two antifundamental insertions in $SU(N)_k$ and $U(N)_k$ theories. These formulae are consistent with the conjectured level-rank, Bose-Fermi duality between these theories and take the form of a $q=e^{frac{ 2 pi i }{kappa}}$ deformation of their large $k$ counterparts. In the 't Hooft large $N$ limit our results reduce to standard rules with one twist: the $S$-matrix in the singlet channel is reduced by the factor $frac{sin pi lambda}{pi lambda} $ (where $lambda$ is the 't Hooft coupling), explaining `anomalous' crossing properties observed in earlier direct large $N$ computations.
我们提出了在$2+1$维中与大质量物质相互作用的chen - simons规范理论的交叉对称规则的一个猜想。我们的交叉规则是根据威尔森线的特定缠结的期望值给出的，并在大的陈-西蒙斯水平上简化为标准规则。对于$SU(N)_k$和$U(N)_k$理论中两个基本插入和两个反基本插入的特殊情况，我们给出了完全明确的结果。这些公式与这些理论之间推测的水平秩、玻色-费米二象性是一致的，并采取了它们巨大的$k$对应物的$q=e^{frac{ 2 pi i }{kappa}}$变形的形式。在't Hooft大$N$限制中，我们的结果通过一个扭曲减少到标准规则:单线态通道中的$S$ -矩阵通过因子$frac{sin pi lambda}{pi lambda} $减少(其中$lambda$是't Hooft耦合)，解释了在早期直接大型$N$计算中观察到的“异常”交叉特性。
{"title":"Crossing symmetry in matter Chern–Simons theories at finite $N$ and $k$","authors":"Umang Mehta, Shiraz Minwalla, Chintan Patel, S. Prakash, Kartik Sharma","doi":"10.4310/atmp.2023.v27.n1.a5","DOIUrl":"https://doi.org/10.4310/atmp.2023.v27.n1.a5","url":null,"abstract":"We present a conjecture for the crossing symmetry rules for Chern-Simons gauge theories interacting with massive matter in $2+1$ dimensions. Our crossing rules are given in terms of the expectation values of particular tangles of Wilson lines, and reduce to the standard rules at large Chern-Simons level. We present completely explicit results for the special case of two fundamental and two antifundamental insertions in $SU(N)_k$ and $U(N)_k$ theories. These formulae are consistent with the conjectured level-rank, Bose-Fermi duality between these theories and take the form of a $q=e^{frac{ 2 pi i }{kappa}}$ deformation of their large $k$ counterparts. In the 't Hooft large $N$ limit our results reduce to standard rules with one twist: the $S$-matrix in the singlet channel is reduced by the factor $frac{sin pi lambda}{pi lambda} $ (where $lambda$ is the 't Hooft coupling), explaining `anomalous' crossing properties observed in earlier direct large $N$ computations.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":"26 14 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90276661","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 : 2022-01-01DOI: 10.4310/atmp.2022.v26.n7.a1
C. Bai, Xing Gao, Li Guo, Yi Zhang
{"title":"Operator forms of the nonhomogeneous associative classical Yang–Baxter equation","authors":"C. Bai, Xing Gao, Li Guo, Yi Zhang","doi":"10.4310/atmp.2022.v26.n7.a1","DOIUrl":"https://doi.org/10.4310/atmp.2022.v26.n7.a1","url":null,"abstract":"","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":"12 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87751716","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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