Pub Date : 2020-11-19DOI: 10.21468/SCIPOSTPHYS.10.3.074
Joe Davighi, Nakarin Lohitsiri
We give a general description of the interplay that can occur between local and global anomalies, in terms of (co)bordism. Mathematically, such an interplay is encoded in the non-canonical splitting of short exact sequences known to classify invertible field theories. We study various examples of the phenomenon in 2, 4, and 6 dimensions. We also describe how this understanding of anomaly interplay provides a rigorous bordism-based version of an old method for calculating global anomalies (starting from local anomalies in a related theory) due to Elitzur and Nair.
{"title":"The algebra of anomaly interplay","authors":"Joe Davighi, Nakarin Lohitsiri","doi":"10.21468/SCIPOSTPHYS.10.3.074","DOIUrl":"https://doi.org/10.21468/SCIPOSTPHYS.10.3.074","url":null,"abstract":"We give a general description of the interplay that can occur between local and global anomalies, in terms of (co)bordism. Mathematically, such an interplay is encoded in the non-canonical splitting of short exact sequences known to classify invertible field theories. We study various examples of the phenomenon in 2, 4, and 6 dimensions. We also describe how this understanding of anomaly interplay provides a rigorous bordism-based version of an old method for calculating global anomalies (starting from local anomalies in a related theory) due to Elitzur and Nair.","PeriodicalId":8443,"journal":{"name":"arXiv: High Energy Physics - Theory","volume":"34 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82988491","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 : 2020-11-18DOI: 10.21468/SCIPOSTPHYS.10.2.049
Ruihua Fan, Yingfei Gu, A. Vishwanath, X. Wen
In this work, we study non-equilibrium dynamics in Floquet conformal field theories (CFTs) in 1+1D, in which the driving Hamiltonian involves the energy-momentum density spatially modulated by an arbitrary smooth function. This generalizes earlier work which was restricted to the sine-square deformed type of Floquet Hamiltonians, operating within a $mathfrak{sl}_2$ sub-algebra. Here we show remarkably that the problem remains soluble in this generalized case which involves the full Virasoro algebra, based on a geometrical approach. It is found that the phase diagram is determined by the stroboscopic trajectories of operator evolution. The presence/absence of spatial fixed points in the operator evolution indicates that the driven CFT is in a heating/non-heating phase, in which the entanglement entropy grows/oscillates in time. Additionally, the heating regime is further subdivided into a multitude of phases, with different entanglement patterns and spatial distribution of energy-momentum density, which are characterized by the number of spatial fixed points. Phase transitions between these different heating phases can be achieved simply by changing the duration of application of the driving Hamiltonian. We demonstrate the general features with concrete CFT examples and compare the results to lattice calculations and find remarkable agreement.
{"title":"Floquet conformal field theories with generally deformed Hamiltonians","authors":"Ruihua Fan, Yingfei Gu, A. Vishwanath, X. Wen","doi":"10.21468/SCIPOSTPHYS.10.2.049","DOIUrl":"https://doi.org/10.21468/SCIPOSTPHYS.10.2.049","url":null,"abstract":"In this work, we study non-equilibrium dynamics in Floquet conformal field theories (CFTs) in 1+1D, in which the driving Hamiltonian involves the energy-momentum density spatially modulated by an arbitrary smooth function. This generalizes earlier work which was restricted to the sine-square deformed type of Floquet Hamiltonians, operating within a $mathfrak{sl}_2$ sub-algebra. Here we show remarkably that the problem remains soluble in this generalized case which involves the full Virasoro algebra, based on a geometrical approach. It is found that the phase diagram is determined by the stroboscopic trajectories of operator evolution. The presence/absence of spatial fixed points in the operator evolution indicates that the driven CFT is in a heating/non-heating phase, in which the entanglement entropy grows/oscillates in time. Additionally, the heating regime is further subdivided into a multitude of phases, with different entanglement patterns and spatial distribution of energy-momentum density, which are characterized by the number of spatial fixed points. Phase transitions between these different heating phases can be achieved simply by changing the duration of application of the driving Hamiltonian. We demonstrate the general features with concrete CFT examples and compare the results to lattice calculations and find remarkable agreement.","PeriodicalId":8443,"journal":{"name":"arXiv: High Energy Physics - Theory","volume":"13 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87116413","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 : 2020-11-17DOI: 10.1142/S0217732321501248
L. Fabbri, R. Rogerio
One of the most important mathematical tools necessary for Quantum Field Theory calculations is the field propagator. Applications are always done in terms of plane waves and although this has furnished many magnificent results, one may still be allowed to wonder what is the form of the most general propagator that can be written. In the present paper we find the most general propagator in the case of vectors and spinors, and in this case whether they are singular or regular, by exploiting what is known to be their polar forms.
{"title":"Most general propagator in quantum field theory","authors":"L. Fabbri, R. Rogerio","doi":"10.1142/S0217732321501248","DOIUrl":"https://doi.org/10.1142/S0217732321501248","url":null,"abstract":"One of the most important mathematical tools necessary for Quantum Field Theory calculations is the field propagator. Applications are always done in terms of plane waves and although this has furnished many magnificent results, one may still be allowed to wonder what is the form of the most general propagator that can be written. In the present paper we find the most general propagator in the case of vectors and spinors, and in this case whether they are singular or regular, by exploiting what is known to be their polar forms.","PeriodicalId":8443,"journal":{"name":"arXiv: High Energy Physics - Theory","volume":"3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80972848","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 : 2020-11-16DOI: 10.21468/SciPostPhys.10.5.122
A. Bose, Aninda Sinha, S. Tiwari
We examine the space of allowed S-matrices on the Adler zeros' plane using the recently resurrected (numerical) S-matrix bootstrap program for pion scattering. Two physical quantities, an averaged total scattering cross-section, and an averaged entanglement power for the boundary S-matrices, are studied. Emerging linearity in the leading Regge trajectory is correlated with a reduction in both these quantities. We identify two potentially viable regions where the S-matrices give decent agreement with low energy S- and P-wave scattering lengths and have leading Regge trajectory compatible with experiments. The Lovelace-Shapiro model, which was a precursor to modern string theory, is given by a straight line in the Adler zeros' plane and, quite remarkably, we find that this line intersects the space of allowed S-matrices near both these regions.
{"title":"Selection rules for the S-Matrix bootstrap","authors":"A. Bose, Aninda Sinha, S. Tiwari","doi":"10.21468/SciPostPhys.10.5.122","DOIUrl":"https://doi.org/10.21468/SciPostPhys.10.5.122","url":null,"abstract":"We examine the space of allowed S-matrices on the Adler zeros' plane using the recently resurrected (numerical) S-matrix bootstrap program for pion scattering. Two physical quantities, an averaged total scattering cross-section, and an averaged entanglement power for the boundary S-matrices, are studied. Emerging linearity in the leading Regge trajectory is correlated with a reduction in both these quantities. We identify two potentially viable regions where the S-matrices give decent agreement with low energy S- and P-wave scattering lengths and have leading Regge trajectory compatible with experiments. The Lovelace-Shapiro model, which was a precursor to modern string theory, is given by a straight line in the Adler zeros' plane and, quite remarkably, we find that this line intersects the space of allowed S-matrices near both these regions.","PeriodicalId":8443,"journal":{"name":"arXiv: High Energy Physics - Theory","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79656530","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 : 2020-11-16DOI: 10.1103/physrevd.103.025001
M. Nitta, S. Sasaki
We formulate four-dimensional $mathcal{N} = 1$ supersymmetric nonlinear sigma models on Hermitian symmetric spaces with higher derivative terms, free from the auxiliary field problem and the Ostrogradski's ghosts, as gauged linear sigma models. We then study Bogomol'nyi-Prasad-Sommerfield equations preserving 1/2 or 1/4 supersymmetries. We find that there are distinct branches, that we call canonical ($F=0$) and non-canonical ($Fneq 0$) branches, associated with solutions to auxiliary fields $F$ in chiral multiplets. For the ${mathbb C}P^N$ model, we obtain a supersymmetric ${mathbb C}P^N$ Skyrme-Faddeev model in the canonical branch while in the non-canonical branch the Lagrangian consists of solely the ${mathbb C}P^N$ Skyrme-Faddeev term without a canonical kinetic term. These structures can be extended to the Grassmann manifold $G_{M,N} = SU(M)/[SU(M-N)times SU(N) times U(1)]$. For other Hermitian symmetric spaces such as the quadric surface $Q^{N-2}=SO(N)/[SO(N-2) times U(1)])$, we impose F-term (holomorphic) constraints for embedding them into ${mathbb C}P^{N-1}$ or Grassmann manifold. We find that these constraints are consistent in the canonical branch but yield additional constraints on the dynamical fields thus reducing the target spaces in the non-canonical branch.
{"title":"Higher derivative supersymmetric nonlinear sigma models on Hermitian symmetric spaces and BPS states therein","authors":"M. Nitta, S. Sasaki","doi":"10.1103/physrevd.103.025001","DOIUrl":"https://doi.org/10.1103/physrevd.103.025001","url":null,"abstract":"We formulate four-dimensional $mathcal{N} = 1$ supersymmetric nonlinear sigma models on Hermitian symmetric spaces with higher derivative terms, free from the auxiliary field problem and the Ostrogradski's ghosts, as gauged linear sigma models. We then study Bogomol'nyi-Prasad-Sommerfield equations preserving 1/2 or 1/4 supersymmetries. We find that there are distinct branches, that we call canonical ($F=0$) and non-canonical ($Fneq 0$) branches, associated with solutions to auxiliary fields $F$ in chiral multiplets. For the ${mathbb C}P^N$ model, we obtain a supersymmetric ${mathbb C}P^N$ Skyrme-Faddeev model in the canonical branch while in the non-canonical branch the Lagrangian consists of solely the ${mathbb C}P^N$ Skyrme-Faddeev term without a canonical kinetic term. These structures can be extended to the Grassmann manifold $G_{M,N} = SU(M)/[SU(M-N)times SU(N) times U(1)]$. For other Hermitian symmetric spaces such as the quadric surface $Q^{N-2}=SO(N)/[SO(N-2) times U(1)])$, we impose F-term (holomorphic) constraints for embedding them into ${mathbb C}P^{N-1}$ or Grassmann manifold. We find that these constraints are consistent in the canonical branch but yield additional constraints on the dynamical fields thus reducing the target spaces in the non-canonical branch.","PeriodicalId":8443,"journal":{"name":"arXiv: High Energy Physics - Theory","volume":"23 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83465335","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}
Kevin Goldstein, Vishnu Jejjala, Y. Lei, S. van Leuven, Wei Li
{"title":"Residues, modularity, and the Cardy limit of the 4d $$ mathcal{N} $$ = 4 superconformal index","authors":"Kevin Goldstein, Vishnu Jejjala, Y. Lei, S. van Leuven, Wei Li","doi":"10.1007/JHEP04(2021)216","DOIUrl":"https://doi.org/10.1007/JHEP04(2021)216","url":null,"abstract":"","PeriodicalId":8443,"journal":{"name":"arXiv: High Energy Physics - Theory","volume":"27 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86977583","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}
Damon J. Binder, Shai M. Chester, Max Jerdee, S. Pufu
{"title":"The 3d $mathcal{N}=6$ Bootstrap: From Higher Spins to Strings to Membranes","authors":"Damon J. Binder, Shai M. Chester, Max Jerdee, S. Pufu","doi":"10.1007/JHEP05(2021)083","DOIUrl":"https://doi.org/10.1007/JHEP05(2021)083","url":null,"abstract":"","PeriodicalId":8443,"journal":{"name":"arXiv: High Energy Physics - Theory","volume":"1 3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86343807","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 : 2020-11-11DOI: 10.1103/PHYSREVD.103.064073
A. Bhatnagar, I. Lovreković
We consider holography of two pp-wave metrics in conformal gravity, their one point functions, and asymptotic symmetries. One of the metrics is a generalization of the standard pp-waves in Einstein gravity to conformal gravity. The holography of this metric shows that within conformal gravity one can have realised solution which has non-vanishing partially massless response (PMR) tensor even for vanishing subleading term in the Fefferman-Graham expansion (i.e. Neumann boundary conditions), and vice-versa.
{"title":"Holography of \u0000pp\u0000 waves in conformal gravity","authors":"A. Bhatnagar, I. Lovreković","doi":"10.1103/PHYSREVD.103.064073","DOIUrl":"https://doi.org/10.1103/PHYSREVD.103.064073","url":null,"abstract":"We consider holography of two pp-wave metrics in conformal gravity, their one point functions, and asymptotic symmetries. One of the metrics is a generalization of the standard pp-waves in Einstein gravity to conformal gravity. The holography of this metric shows that within conformal gravity one can have realised solution which has non-vanishing partially massless response (PMR) tensor even for vanishing subleading term in the Fefferman-Graham expansion (i.e. Neumann boundary conditions), and vice-versa.","PeriodicalId":8443,"journal":{"name":"arXiv: High Energy Physics - Theory","volume":"20 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91009058","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 : 2020-11-11DOI: 10.1103/PhysRevD.103.106011
S. Cremonini, Callum R. T. Jones, James T. Liu, B. McPeak, Yuezhang Tang
We analyze the constraints on four-derivative corrections to 5d Einstein-Maxwell theory from the black hole Weak Gravity Conjecture (WGC). We calculate the leading corrections to the extremal mass of asymptotically flat 5d charged solutions as well as 4d Kaluza-Klein compactifications. The WGC bounds from the latter, interpreted as 4d dyonic black holes, are found to be strictly stronger. As magnetic graviphoton charge lifts to a NUT-like charge in 5d, we argue that the logic of the WGC should apply to these topological charges as well and leads to new constraints on purely gravitational theories.
{"title":"NUT charge weak gravity conjecture from dimensional reduction","authors":"S. Cremonini, Callum R. T. Jones, James T. Liu, B. McPeak, Yuezhang Tang","doi":"10.1103/PhysRevD.103.106011","DOIUrl":"https://doi.org/10.1103/PhysRevD.103.106011","url":null,"abstract":"We analyze the constraints on four-derivative corrections to 5d Einstein-Maxwell theory from the black hole Weak Gravity Conjecture (WGC). We calculate the leading corrections to the extremal mass of asymptotically flat 5d charged solutions as well as 4d Kaluza-Klein compactifications. The WGC bounds from the latter, interpreted as 4d dyonic black holes, are found to be strictly stronger. As magnetic graviphoton charge lifts to a NUT-like charge in 5d, we argue that the logic of the WGC should apply to these topological charges as well and leads to new constraints on purely gravitational theories.","PeriodicalId":8443,"journal":{"name":"arXiv: High Energy Physics - Theory","volume":"84 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88156513","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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