Superconformal index, BPS monodromy and chiral algebras

Sergio Cecotti; Jaewon Song; Cumrun Vafa; Wenbin Yan

doi:10.1007/jhep11(2017)013

A 4d $$ \mathcal{N} $$ = 1 Cardy Formula

Journal of High Energy Physics ◽

10.1007/jhep01(2021)025 ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Joonho Kim ◽

Seok Kim ◽

Jaewon Song

Keyword(s):

Black Holes ◽

Free Energy ◽

Asymptotic Behavior ◽

High Temperature ◽

Gauge Theory ◽

Chemical Potential ◽

Temperature Limit ◽

Superconformal Index ◽

High Temperature Limit ◽

Cardy Formula

Abstract We study the asymptotic behavior of the (modified) superconformal index for 4d $$ \mathcal{N} $$ N = 1 gauge theory. By considering complexified chemical potential, we find that the ‘high-temperature limit’ of the index can be written in terms of the conformal anomalies 3c − 2a. We also find macroscopic entropy from our asymptotic free energy when the Hofman-Maldacena bound 1/2 < a/c < 3/2 for the interacting SCFT is satisfied. We study $$ \mathcal{N} $$ N = 1 theories that are dual to AdS5 × Yp,p and find that the Cardy limit of our index accounts for the Bekenstein-Hawking entropy of large black holes.

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The Coulomb and Higgs branches of $$ \mathcal{N} $$ = 1 theories of Class $$ {\mathcal{S}}_k $$

Journal of High Energy Physics ◽

10.1007/jhep02(2021)137 ◽

2021 ◽

Vol 2021 (2) ◽

Author(s):

Thomas Bourton ◽

Alessandro Pini ◽

Elli Pomoni

Keyword(s):

String Theory ◽

Special Class ◽

Hilbert Series ◽

Superconformal Index

Abstract Even though for generic $$ \mathcal{N} $$ N = 1 theories it is not possible to separate distinct branches of supersymmetric vacua, in this paper we study a special class of $$ \mathcal{N} $$ N = 1 SCFTs, these of Class $$ {\mathcal{S}}_k $$ S k for which it is possible to define Coulomb and Higgs branches precisely as for the $$ \mathcal{N} $$ N = 2 theories of Class $$ \mathcal{S} $$ S from which they descend. We study the BPS operators that parameterise these branches of vacua using the different limits of the superconformal index as well as the Coulomb and Higgs branch Hilbert Series. Finally, with the tools we have developed, we provide a check that six dimensional (1, 1) Little String theory can be deconstructed from a toroidal quiver in Class $$ {\mathcal{S}}_k $$ S k .

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The large-N limit of the 4d $$ \mathcal{N} $$ = 1 superconformal index

Journal of High Energy Physics ◽

10.1007/jhep11(2020)150 ◽

2020 ◽

Vol 2020 (11) ◽

Author(s):

Alejandro Cabo-Bizet ◽

Davide Cassani ◽

Dario Martelli ◽

Sameer Murthy

Keyword(s):

Effective Action ◽

Black Hole Solution ◽

Saddle Points ◽

Unitary Matrix ◽

Finite Abelian Groups ◽

Superconformal Index ◽

Cubic Form ◽

Chemical Potentials ◽

Large N ◽

Superconformal Theories

Abstract We systematically analyze the large-N limit of the superconformal index of $$ \mathcal{N} $$ N = 1 superconformal theories having a quiver description. The index of these theories is known in terms of unitary matrix integrals, which we calculate using the recently-developed technique of elliptic extension. This technique allows us to easily evaluate the integral as a sum over saddle points of an effective action in the limit where the rank of the gauge group is infinite. For a generic quiver theory under consideration, we find a special family of saddles whose effective action takes a universal form controlled by the anomaly coefficients of the theory. This family includes the known supersymmetric black hole solution in the holographically dual AdS5 theories. We then analyze the index refined by turning on flavor chemical potentials. We show that, for a certain range of chemical potentials, the effective action again takes a universal cubic form that is controlled by the anomaly coefficients of the theory. Finally, we present a large class of solutions to the saddle-point equations which are labelled by group homomorphisms of finite abelian groups of order N into the torus.

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THE ANNIHILATING IDEALS OF MINIMAL MODELS

International Journal of Modern Physics A ◽

10.1142/s0217751x92003793 ◽

1992 ◽

Vol 07 (supp01a) ◽

pp. 217-238 ◽

Cited By ~ 53

Author(s):

BORIS L. FEIGIN ◽

TOMOKI NAKANISHI ◽

HIROSI OOGURI

Keyword(s):

Central Charge ◽

Field Theories ◽

Conformal Field Theories ◽

Minimal Models ◽

Finite Models ◽

Conformal Field ◽

Intimate Relation ◽

Chiral Algebras

We describe several aspects of the annihilating ideals and reduced chiral algebras of conformal field theories, especially, minimal models of Wn algebras. The structure of the annihilating ideal and a vanishing condition is given. Using the annihilating ideal, the structure of quasi-finite models of the Virasoro (2,q) minimal models are studied, and their intimate relation to the Gordon identities are discussed. We also show the examples in which the reduced algebras of Wn and Wℓ algebras at the same central charge are isomorphic to each other.

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