scholarly journals 4D and 2D superconformal index with surface operator

2011 ◽  
Vol 2011 (8) ◽  
Author(s):  
Yu Nakayama
Keyword(s):  
Superconformal Index ◽  
Surface Operator

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

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.

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

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 .

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

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.

scholarly journals Surface defects, the superconformal index and q-deformed Yang-Mills

2013 ◽  
Vol 2013 (10) ◽  
Author(s):  
Luis F. Alday ◽  
Mathew Bullimore ◽  
Martin Fluder ◽  
Lotte Hollands
Keyword(s):  
Surface Defects ◽  
Yang Mills ◽  
Superconformal Index

scholarly journals Spectra of elliptic potentials and supersymmetric gauge theories

2020 ◽  
Vol 2020 (8) ◽  
Author(s):  
Wei He
Keyword(s):  
Gauge Theory ◽  
Strong Coupling ◽  
Moduli Space ◽  
Gauge Theories ◽  
Duality Transformations ◽  
Spectral Solution ◽  
Supersymmetric Gauge ◽  
Strong Coupling Expansions ◽  
Surface Operator ◽  
Function Potential

Abstract We study a relation between asymptotic spectra of the quantum mechanics problem with a four components elliptic function potential, the Darboux-Treibich-Verdier (DTV) potential, and the Omega background deformed N=2 supersymmetric SU(2) QCD models with four massive flavors in the Nekrasov-Shatashvili limit. The weak coupling spectral solution of the DTV potential is related to the instanton partition function of supersymmetric QCD with surface operator. There are two strong coupling spectral solutions of the DTV potential, they are related to the strong coupling expansions of gauge theory prepotential at the magnetic and dyonic points in the moduli space. A set of duality transformations relate the two strong coupling expansions for spectral solution, and for gauge theory prepotential.

scholarly journals M2-branes and AdS/CFT: A review

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Kazuo Hosomichi
Keyword(s):  
Black Holes ◽  
Free Energy ◽  
Superconformal Index ◽  
Charged Black Holes ◽  
Large N

Abstract We briefly review some of the important developments in the last decade in the theory of multiple M2-branes and $\text{AdS}_4/\text{CFT}_3$ correspondence. Taking the examples of the superconformal index, free energy on $S^3$, and entropy of charged black holes, we illustrate how the large-$N$ limit was studied and the correspondence was checked.

scholarly journals Finite-N corrections to the superconformal index of toric quiver gauge theories

2020 ◽  
Vol 2020 (4) ◽  
Author(s):  
Reona Arai ◽  
Shota Fujiwara ◽  
Yosuke Imamura ◽  
Tatsuya Mori
Keyword(s):  
Gauge Theory ◽  
Gauge Theories ◽  
Gauge Groups ◽  
Superconformal Index

Abstract The superconformal index of quiver gauge theories realized on D3-branes in toric Calabi–Yau cones is investigated. We use the AdS/CFT correspondence and study D3-branes wrapped on supersymmetric cycles. We focus on brane configurations in which a single D3-brane is wrapped on a cycle, and we do not take account of branes with multiple wrapping. We propose a formula that gives finite-$N$ corrections to the index caused by such brane configurations. We compare the predictions of the formula for several examples with the results on the gauge theory side obtained by using localization for small sizes of gauge groups, and confirm that the formula correctly reproduces the finite-$N$ corrections up to the expected order.

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