Pub Date : 2020-09-26DOI: 10.1142/S0217751X21500494
V. Dobrev
The main purpose of the present paper is to lay the foundations of generalizing the AdS/CFT (holography) idea beyond the conformal setting. The main tool is to find suitable realizations of the bulk and boundary via group theory. We use all ten families of classical real semisimple Lie groups $G$ and Lie algebras $cal G$. For this are used several group and algebra decompositions: the global Iwasawa decomposition and the local Bruhat and Sekiguchi-like decomposititions. The same analysis is applied to the exceptional real semisimple Lie algebras.
{"title":"Tenfold way for holography: AdS/CFT and beyond","authors":"V. Dobrev","doi":"10.1142/S0217751X21500494","DOIUrl":"https://doi.org/10.1142/S0217751X21500494","url":null,"abstract":"The main purpose of the present paper is to lay the foundations of generalizing the AdS/CFT (holography) idea beyond the conformal setting. The main tool is to find suitable realizations of the bulk and boundary via group theory. We use all ten families of classical real semisimple Lie groups $G$ and Lie algebras $cal G$. For this are used several group and algebra decompositions: the global Iwasawa decomposition and the local Bruhat and Sekiguchi-like decomposititions. The same analysis is applied to the exceptional real semisimple Lie algebras.","PeriodicalId":8443,"journal":{"name":"arXiv: High Energy Physics - Theory","volume":"50 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90754124","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Algebra of quantum $$ mathcal{C} $$-polynomials","authors":"A. Mironov, A. Morozov","doi":"10.1007/JHEP02(2021)142","DOIUrl":"https://doi.org/10.1007/JHEP02(2021)142","url":null,"abstract":"","PeriodicalId":8443,"journal":{"name":"arXiv: High Energy Physics - Theory","volume":"55 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82313779","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-09-24DOI: 10.1103/physrevd.102.106022
K. S. Rigatos
We show that the $AdS_5 times L^{a,b,c}$ solution in type IIB theory is non-integrable. To do so, we consider a string embedding and study its fluctuations which do not admit Liouville integrable solutions. We, also, perform a numerical analysis to study the time evolution of the string and compute the largest Lyapunov exponent. This analysis indicates that the string motion is chaotic. Finally, we consider the point-like limit of the string that corresponds to BPS mesons of the quiver theory.
{"title":"Nonintegrability of \u0000La,b,c\u0000 quiver gauge theories","authors":"K. S. Rigatos","doi":"10.1103/physrevd.102.106022","DOIUrl":"https://doi.org/10.1103/physrevd.102.106022","url":null,"abstract":"We show that the $AdS_5 times L^{a,b,c}$ solution in type IIB theory is non-integrable. To do so, we consider a string embedding and study its fluctuations which do not admit Liouville integrable solutions. We, also, perform a numerical analysis to study the time evolution of the string and compute the largest Lyapunov exponent. This analysis indicates that the string motion is chaotic. Finally, we consider the point-like limit of the string that corresponds to BPS mesons of the quiver theory.","PeriodicalId":8443,"journal":{"name":"arXiv: High Energy Physics - Theory","volume":"10 1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83611022","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-09-23DOI: 10.1142/s0217751x20502061
Yoshiharu Kawamura, Yasunari Nishikawa
We study diagonal representatives of boundary condition matrices on the orbifolds $S^1/Z_2$ and $T^2/Z_m$ ($m=2, 3, 4, 6$). We give an alternative proof of the existence of diagonal representatives in each equivalent class of boundary condition matrices on $S^1/Z_2$, using a matrix exponential representation, and show that they do not necessarily exist on $T^2/Z_2$, $T^2/Z_3$, and $T^2/Z_4$. Each equivalence class on $T^2/Z_6$ has a diagonal representative, because its boundary conditions are determined by a single unitary matrix.
{"title":"On diagonal representatives in boundary condition matrices on orbifolds","authors":"Yoshiharu Kawamura, Yasunari Nishikawa","doi":"10.1142/s0217751x20502061","DOIUrl":"https://doi.org/10.1142/s0217751x20502061","url":null,"abstract":"We study diagonal representatives of boundary condition matrices on the orbifolds $S^1/Z_2$ and $T^2/Z_m$ ($m=2, 3, 4, 6$). We give an alternative proof of the existence of diagonal representatives in each equivalent class of boundary condition matrices on $S^1/Z_2$, using a matrix exponential representation, and show that they do not necessarily exist on $T^2/Z_2$, $T^2/Z_3$, and $T^2/Z_4$. Each equivalence class on $T^2/Z_6$ has a diagonal representative, because its boundary conditions are determined by a single unitary matrix.","PeriodicalId":8443,"journal":{"name":"arXiv: High Energy Physics - Theory","volume":"46 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88324203","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-09-23DOI: 10.1103/PHYSREVD.103.085003
G. Prokhorov, O. Teryaev, V. Zakharov
We consider photonic vortical effect, i.e. the difference of the flows of left- and right-handed photons along the vector of angular velocity in rotating photonic medium. Two alternative frameworks to evaluate the effect are considered, both of which have already been tried in the literature. First, the standard thermal fied theory and, alternatively, Hawking-radiation-type derivation. In our earlier attempt to compare the two approaches, we found a crucial factor of two difference. Here we revisit the problem, paying more attention to details of infrared regularizations. We find out that introduction of an infinitesimal mass of the vector field brings the two ways of evaluating the chiral vortical effect into agreement with each other. Some implications, both on the theoretical and phenomenological sides, are mentioned.
{"title":"Chiral vortical effect for vector fields","authors":"G. Prokhorov, O. Teryaev, V. Zakharov","doi":"10.1103/PHYSREVD.103.085003","DOIUrl":"https://doi.org/10.1103/PHYSREVD.103.085003","url":null,"abstract":"We consider photonic vortical effect, i.e. the difference of the flows of left- and right-handed photons along the vector of angular velocity in rotating photonic medium. Two alternative frameworks to evaluate the effect are considered, both of which have already been tried in the literature. First, the standard thermal fied theory and, alternatively, Hawking-radiation-type derivation. In our earlier attempt to compare the two approaches, we found a crucial factor of two difference. Here we revisit the problem, paying more attention to details of infrared regularizations. We find out that introduction of an infinitesimal mass of the vector field brings the two ways of evaluating the chiral vortical effect into agreement with each other. Some implications, both on the theoretical and phenomenological sides, are mentioned.","PeriodicalId":8443,"journal":{"name":"arXiv: High Energy Physics - Theory","volume":"49 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87178735","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-09-23DOI: 10.1103/PHYSREVD.103.026014
Suvankar Dutta, Taniya Mandal, Sanhita Parihar
The Rivlin-Ericksen model is one of the oldest models in fluid dynamics to describe non-Newtonian properties. The model comes with two independent transports at second order. In this paper, we study the relativistic origin of the Rivlin-Ericksen fluid. Starting from a relativistic Weyl invariant uncharged fluid in $3+1$ dimensions, we reduce it over light-cone directions and obtain a generic non-relativistic uncharged fluid in one lower dimension with all possible second order terms in the constitutive relations. We observe that the Rivlin-Ericksen fluid is a subclass of our generalised non-relativistic system. We also compute the holographic values of all the non-relativistic second order transports and find that three of them satisfy a universal constraint relation.
{"title":"Holographic constraints on generalized Rivlin-Ericksen fluid","authors":"Suvankar Dutta, Taniya Mandal, Sanhita Parihar","doi":"10.1103/PHYSREVD.103.026014","DOIUrl":"https://doi.org/10.1103/PHYSREVD.103.026014","url":null,"abstract":"The Rivlin-Ericksen model is one of the oldest models in fluid dynamics to describe non-Newtonian properties. The model comes with two independent transports at second order. In this paper, we study the relativistic origin of the Rivlin-Ericksen fluid. Starting from a relativistic Weyl invariant uncharged fluid in $3+1$ dimensions, we reduce it over light-cone directions and obtain a generic non-relativistic uncharged fluid in one lower dimension with all possible second order terms in the constitutive relations. We observe that the Rivlin-Ericksen fluid is a subclass of our generalised non-relativistic system. We also compute the holographic values of all the non-relativistic second order transports and find that three of them satisfy a universal constraint relation.","PeriodicalId":8443,"journal":{"name":"arXiv: High Energy Physics - Theory","volume":"26 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73451377","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-09-22DOI: 10.1007/978-3-030-51197-5_4
C. Rovelli
{"title":"Gauge Is More Than Mathematical Redundancy","authors":"C. Rovelli","doi":"10.1007/978-3-030-51197-5_4","DOIUrl":"https://doi.org/10.1007/978-3-030-51197-5_4","url":null,"abstract":"","PeriodicalId":8443,"journal":{"name":"arXiv: High Energy Physics - Theory","volume":"15 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89331730","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-09-21DOI: 10.1103/physrevd.102.125006
Cesim K. Dumlu
We compute the semiclassical decay rate for Kerr black hole by deriving a one-way connection formula, relating the near horizon solution to the outgoing solution at infinity. In particular, we discuss the relevance of the Stokes phenomenon and show how it leads to a Boltzmann-like thermal weight factor by making use of the Stokes diagrams. We also give the exact result for the semiclassical greybody factor $e^{-2S}, $ where $S$ is the leading order WKB action. We contrast our results with Maldacena and Strominger's work [Phys. Rev. D 56, 4975 (1997)], where the emission spectrum for a rotating black hole was computed locally via asymptotic matching. We find that the relative error of semiclassical decay rate with respect to asymptotic matching formula diminishes in the limit of large angular momentum, $l$, as expected. In this limit, the action assumes a compact form: $2S sim (2 l+1) (text{Log} left( frac{16 }{z_0}right)-1)$, where $z_0$ is the cross ratio formed by the critical points (zeroes) of the scattering potential.
{"title":"Stokes phenomenon and Hawking radiation","authors":"Cesim K. Dumlu","doi":"10.1103/physrevd.102.125006","DOIUrl":"https://doi.org/10.1103/physrevd.102.125006","url":null,"abstract":"We compute the semiclassical decay rate for Kerr black hole by deriving a one-way connection formula, relating the near horizon solution to the outgoing solution at infinity. In particular, we discuss the relevance of the Stokes phenomenon and show how it leads to a Boltzmann-like thermal weight factor by making use of the Stokes diagrams. We also give the exact result for the semiclassical greybody factor $e^{-2S}, $ where $S$ is the leading order WKB action. We contrast our results with Maldacena and Strominger's work [Phys. Rev. D 56, 4975 (1997)], where the emission spectrum for a rotating black hole was computed locally via asymptotic matching. We find that the relative error of semiclassical decay rate with respect to asymptotic matching formula diminishes in the limit of large angular momentum, $l$, as expected. In this limit, the action assumes a compact form: $2S sim (2 l+1) (text{Log} left( frac{16 }{z_0}right)-1)$, where $z_0$ is the cross ratio formed by the critical points (zeroes) of the scattering potential.","PeriodicalId":8443,"journal":{"name":"arXiv: High Energy Physics - Theory","volume":"29 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87914749","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 study the moduli space volume of BPS vortices in quiver gauge theories on compact Riemann surfaces. The existence of BPS vortices imposes constraints on the quiver gauge theories. We show that the moduli space volume is given by a vev of a suitable cohomological operator (volume operator) in a supersymmetric quiver gauge theory, where BPS equations of the vortices are embedded. In the supersymmetric gauge theory, the moduli space volume is exactly evaluated as a contour integral by using the localization. Graph theory is useful to construct the supersymmetric quiver gauge theory and to derive the volume formula. The contour integral formula of the volume (generalization of the Jeffrey-Kirwan residue formula) leads to the Bradlow bounds (upper bounds on the vorticity by the area of the Riemann surface divided by the intrinsic size of the vortex). We give some examples of various quiver gauge theories and discuss properties of the moduli space volume in these theories. Our formula are applied to the volume of the vortex moduli space in the gauged non-linear sigma model with $CP^N$ target space, which is obtained by a strong coupling limit of a parent quiver gauge theory. We also discuss a non-Abelian generalization of the quiver gauge theory and "Abelianization" of the volume formula.
{"title":"The volume of the quiver vortex moduli space","authors":"Kazutoshi Ohta, N. Sakai","doi":"10.1093/PTEP/PTAB012","DOIUrl":"https://doi.org/10.1093/PTEP/PTAB012","url":null,"abstract":"We study the moduli space volume of BPS vortices in quiver gauge theories on compact Riemann surfaces. The existence of BPS vortices imposes constraints on the quiver gauge theories. We show that the moduli space volume is given by a vev of a suitable cohomological operator (volume operator) in a supersymmetric quiver gauge theory, where BPS equations of the vortices are embedded. In the supersymmetric gauge theory, the moduli space volume is exactly evaluated as a contour integral by using the localization. Graph theory is useful to construct the supersymmetric quiver gauge theory and to derive the volume formula. The contour integral formula of the volume (generalization of the Jeffrey-Kirwan residue formula) leads to the Bradlow bounds (upper bounds on the vorticity by the area of the Riemann surface divided by the intrinsic size of the vortex). We give some examples of various quiver gauge theories and discuss properties of the moduli space volume in these theories. Our formula are applied to the volume of the vortex moduli space in the gauged non-linear sigma model with $CP^N$ target space, which is obtained by a strong coupling limit of a parent quiver gauge theory. We also discuss a non-Abelian generalization of the quiver gauge theory and \"Abelianization\" of the volume formula.","PeriodicalId":8443,"journal":{"name":"arXiv: High Energy Physics - Theory","volume":"45 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87106484","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-09-18DOI: 10.1103/PhysRevD.103.106016
Yuta Hamada, J. Pawlowski, M. Yamada
We study anomalous chiral symmetry breaking in two-flavour QCD induced by gravitational and QCD-instantons within asymptotically safe gravity within the functional renormalisation group approach. Similarly to QCD-instantons, gravitational ones, associated to a K3-surface connected by a wormhole-like throat in flat spacetime, generate contributions to the 't~Hooft coupling proportional to $exp(-1/g_N)$ with the dimensionless Newton coupling $g_N$. Hence, in the asymptotically safe gravity scenario with a non-vanishing fixed point coupling $g_N^*$, the induced 't Hooft coupling is finite at the Planck scale, and its size depends on the chosen UV-completion. Within this scenario the gravitational effects on anomalous $U(1)_A$-breaking at the Planck scale may survive at low energy scales. In turn, fermion masses of the order of the Planck scale cannot be present. This constrains the allowed asymptotically safe UV-completion of the Gravity-QCD system. We map-out the parameter regime that is compatible with the existence of light fermions in the low-energy regime.
{"title":"Gravitational instantons and anomalous chiral symmetry breaking","authors":"Yuta Hamada, J. Pawlowski, M. Yamada","doi":"10.1103/PhysRevD.103.106016","DOIUrl":"https://doi.org/10.1103/PhysRevD.103.106016","url":null,"abstract":"We study anomalous chiral symmetry breaking in two-flavour QCD induced by gravitational and QCD-instantons within asymptotically safe gravity within the functional renormalisation group approach. Similarly to QCD-instantons, gravitational ones, associated to a K3-surface connected by a wormhole-like throat in flat spacetime, generate contributions to the 't~Hooft coupling proportional to $exp(-1/g_N)$ with the dimensionless Newton coupling $g_N$. Hence, in the asymptotically safe gravity scenario with a non-vanishing fixed point coupling $g_N^*$, the induced 't Hooft coupling is finite at the Planck scale, and its size depends on the chosen UV-completion. Within this scenario the gravitational effects on anomalous $U(1)_A$-breaking at the Planck scale may survive at low energy scales. In turn, fermion masses of the order of the Planck scale cannot be present. This constrains the allowed asymptotically safe UV-completion of the Gravity-QCD system. We map-out the parameter regime that is compatible with the existence of light fermions in the low-energy regime.","PeriodicalId":8443,"journal":{"name":"arXiv: High Energy Physics - Theory","volume":"71 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74022473","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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