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 The superconformal index and an elliptic algebra of surface defects

2014 ◽  
Vol 2014 (10) ◽  
Author(s):  
Mathew Bullimore ◽  
Martin Fluder ◽  
Lotte Hollands ◽  
Paul Richmond
Keyword(s):  
Surface Defects ◽  
Superconformal Index ◽  
Elliptic Algebra

scholarly journals DUALITY DOMAIN WALL INDEX ON S1 × S3

2013 ◽  
Vol 21 ◽  
pp. 182-183 ◽  
Author(s):  
EUNKYUNG KOH
Keyword(s):  
Domain Wall ◽  
Yang Mills ◽  
Superconformal Index ◽  
Super Yang Mills Theory

We calculate a superconformal index of the half-BPS duality domain wall inserted at the great S2 of S3 in [Formula: see text]SU(2) super Yang-Mills theory on S1 × S3.

scholarly journals Four Dimensional Superconformal Index fromq-Deformed Two Dimensional Yang-Mills Theory

2011 ◽  
Vol 106 (24) ◽  
Author(s):  
Abhijit Gadde ◽  
Leonardo Rastelli ◽  
Shlomo S. Razamat ◽  
Wenbin Yan
Keyword(s):  
Two Dimensional ◽  
Yang Mills ◽  
Superconformal Index

scholarly journals Residues, modularity, and the Cardy limit of the 4d $$ \mathcal{N} $$ = 4 superconformal index

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Kevin Goldstein ◽  
Vishnu Jejjala ◽  
Yang Lei ◽  
Sam van Leuven ◽  
Wei Li
Keyword(s):  
Black Hole ◽  
Chemical Potential ◽  
Specific Region ◽  
Partition Functions ◽  
Potential Space ◽  
Leading Order ◽  
Yang Mills ◽  
Superconformal Index ◽  
Chemical Potentials ◽  
Entropy Functions

Abstract We compute the superconformal index of the $$ \mathcal{N} $$ N = 4 SU(N) Yang-Mills theory through a residue calculation. The method is similar in spirit to the Bethe Ansatz formalism, except that all poles are explicitly known, and we do not require specialization of any of the chemical potentials. Our expression for the index allows us to revisit the Cardy limit using modular properties of four-dimensional supersymmetric partition functions. We find that all residues contribute at leading order in the Cardy limit. In a specific region of flavour chemical potential space, close to the two unrefined points, in fact all residues contribute universally. These universal residues precisely agree with the entropy functions of the asymptotically AdS5 black hole and its “twin saddle” respectively. Finally, we discuss how our formula is suited to study the implications of four-dimensional modularity for the index beyond the Cardy limit.

scholarly journals The Bethe-Ansatz approach to the $$ \mathcal{N} $$ = 4 superconformal index at finite rank

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Alfredo González Lezcano ◽  
Junho Hong ◽  
James T. Liu ◽  
Leopoldo A. Pando Zayas
Keyword(s):  
Gauge Group ◽  
Bethe Ansatz ◽  
Finite Rank ◽  
Yang Mills ◽  
Superconformal Index ◽  
Interesting Pattern ◽  
Ansatz Approach ◽  
Standard Solutions

Abstract We investigate the Bethe-Ansatz approach to the superconformal index of $$ \mathcal{N} $$ N = 4 supersymmetric Yang-Mills with SU(N) gauge group in the context of finite rank, N. We explicitly explore the role of the various types of solutions to the Bethe-Ansatz Equations in recovering the exact index for N = 2, 3. We classify the Bethe-Ansatz Equations solutions as standard (corresponding to a freely acting orbifold T2/ℤm× ℤn) and non-standard. For N = 2, we find that the index is fully recovered by standard solutions and displays an interesting pattern of cancellations. However, for N ≥ 3, the standard solutions alone do not suffice to reconstruct the index. We present quantitative arguments in various regimes of fugacities that highlight the challenging role played by the continuous families of non-standard solutions.

scholarly journals SL(3, ℤ) Modularity and New Cardy limits of the $$ \mathcal{N} $$ = 4 superconformal index

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Vishnu Jejjala ◽  
Yang Lei ◽  
Sam van Leuven ◽  
Wei Li
Keyword(s):  
Field Theory ◽  
Black Holes ◽  
Black Hole ◽  
Parameter Family ◽  
Similar Form ◽  
Four Dimensions ◽  
Yang Mills ◽  
Superconformal Index ◽  
Super Yang Mills Theory

Abstract The entropy of 1/16-th BPS AdS5 black holes can be microscopically accounted for by the superconformal index of the $$ \mathcal{N} $$ N = 4 super-Yang-Mills theory. One way to compute this is through a Cardy-like limit of a formula for the index obtained in [1] using the “S-transformation” of the elliptic Γ function. In this paper, we derive more general SL(3, ℤ) modular properties of the elliptic Γ function. We then use these properties to obtain a three integer parameter family of generalized Cardy-like limits of the $$ \mathcal{N} $$ N = 4 superconformal index. From these limits, we obtain entropy formulae that have a similar form as that of the original AdS5 black hole, up to an overall rescaling of the entropy. We interpret this both on the field theory and the gravitational side. Finally, we comment on how our work suggests a generalization of the Farey tail to four dimensions.

scholarly journals Bootstrapping the superconformal index with surface defects

2013 ◽  
Vol 2013 (1) ◽  
Author(s):  
Davide Gaiotto ◽  
Leonardo Rastelli ◽  
Shlomo S. Razamat
Keyword(s):  
Surface Defects ◽  
Superconformal Index

scholarly journals Superconformal index with surface defects for class Sk

2021 ◽  
Vol 962 ◽  
pp. 115277
Author(s):  
Yuto Ito ◽  
Yutaka Yoshida
Keyword(s):  
Surface Defects ◽  
Superconformal Index

scholarly journals Surface defects from fractional branes. Part II

2020 ◽  
Vol 2020 (8) ◽  
Author(s):  
S.K. Ashok ◽  
M. Billò ◽  
M. Frau ◽  
A. Lerda ◽  
S. Mahato
Keyword(s):  
String Theory ◽  
Surface Defect ◽  
Surface Defects ◽  
Closed String ◽  
Brane World ◽  
Type Ii ◽  
Yang Mills ◽  
Background Values ◽  
World Volume ◽  
Set Up

Abstract A generic half-BPS surface defect of $$ \mathcal{N} $$ N = 4 supersymmetric U(N ) Yang- Mills theory is described by a partition of N = n1 + . . . + nM and a set of 4M continuous parameters. We show that such a defect can be realized by nI stacks of fractional D3-branes in Type II B string theory on a ℤM orbifold background in which the brane world-volume is partially extended along the orbifold directions. In this set up we show that the 4M continuous parameters correspond to constant background values of certain twisted closed string scalars of the orbifold. These results extend and generalize what we have presented for the simple defects in a previous paper.

scholarly journals Superconformal index of low-rank gauge theories via the Bethe Ansatz

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Francesco Benini ◽  
Giovanni Rizi
Keyword(s):  
Gauge Group ◽  
Bethe Ansatz ◽  
Gauge Theories ◽  
Low Rank ◽  
Continuous Family ◽  
Yang Mills ◽  
Superconformal Index ◽  
All Solutions ◽  
One To One

Abstract We study the Bethe Ansatz formula for the superconformal index, in the case of 4d $$ \mathcal{N} $$ N = 4 super-Yang-Mills with gauge group SU(N). We observe that not all solutions to the Bethe Ansatz Equations (BAEs) contribute to the index, and thus formulate “reduced BAEs” such that all and only their solutions contribute. We then propose, sharpening a conjecture of Arabi Ardehali et al. [1], that there is a one-to-one correspondence between branches of solutions to the reduced BAEs and vacua of the 4d $$ \mathcal{N} $$ N = 1* theory. We test the proposal in the case of SU(2) and SU(3). In the case of SU(3), we confirm that there is a continuous family of solutions, whose contribution to the index is non-vanishing.

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