Applications of the superconformal index for protected operators and q-hypergeometric identities to N=1 dual theories

By F. Dolan, H. Osborn, Institiúid Ard-Léinn Bhailé, Atha Cliath. 2008

389 citations recorded by the source corpus.

Abstract The results of Romelsberger for an N = 1 superconformal index counting protected operators, satisfying a BPS condition and which cannot be combined to form long multiplets, are analysed further. The index is expressible in terms of single particle superconformal characters for N = 1 scalar and vector multiplets. For SQCD, involving SU ( N c ) gauge groups and appropriate numbers of flavours N f , the formula used to construct the index may be proved to give identical results for theories linked by Seiberg duality using recently proved theorems for q -series elliptic hypergeometric integrals. The discussion is also extended to Kutasov–Schwimmer dual theories in the large N c , N f limit and to dual theories with Sp ( N ) and SO ( N ) gauge groups. For the former, a transformation identity for elliptic hypergeometric integrals directly verifies that the index is the same for the electric and magnetic theory. For SO ( N ) theories the corresponding result may also be obtained from the same basic identity. An expansion of the index to several orders is also obtained in a form where the detailed protected operator content may be read off. Relevant mathematical results are reviewed.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/4c47ae2cb36e1e943e27928b753c724ba2483e49

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Nuclear and High Energy Physics

Citations in the corpus

Localization on Hopf surfaces (2014, neutral): “Extending to general p, q a prescription given therein for p = q, we find that our Esusy can be expressed in terms of the letter indices [12, 14, 25]”
Supersymmetry on curved spaces and holography (2012, background): “For the physicist after the mid-90ies an almost trivial thing, identifying the index for two Seiberg dual phases of the same theory turns out to be at the edge of knowledge for the mathematicians [24, 25].”
The gravity dual of supersymmetric gauge theories on a squashed three-sphere (2011, methodology): “theories may be computed by putting the theories on S × S [5, 6, 7] and S × S [8, 9, 10, 11], respectively.”
Gauge Theories and Macdonald Polynomials (2011, background): “Dolan and Osborn’s beautiful results on superconformal representation theory and on the index were a direct influence and inspiration for our work.”
Elliptic Hypergeometry of Supersymmetric Dualities (2009, methodology): “For these theories we have the following indices (in the renormalized variables) [26]”
N$$ \mathcal{N} $$ = 1 supersymmetric indices and the four-dimensional A-model (2017, background): “This is the standard expression for the S3 supersymmetric index [2, 34] with p = q = q.”
Bootstrapping the superconformal index with surface defects (2012, background): “The relevance of these functions to the index computations was observed in [41].”
Comments on 3d Seiberg-like dualities (2011, methodology): “5) By means of a trick analogous to that used in [59] for the superconformal indices of 4d gauge theories, we can reduce the partition functions of the orthogonal gauge theories to those of symplectic gauge theories with fundamental matter (7.”
Microscopic origin of the Bekenstein-Hawking entropy of supersymmetric AdS5 black holes (2018, methodology): “When n = 0, we immediately see that I reduces to the usual expression of the Hamiltonian index [62].”
Relation between the 4d superconformal index and the S3 partition function (2011, methodology): “This quantity is exactly calculable, and is conveniently used as a tool to check Seiberg-duality[15, 16, 17, 18] and AdS5/CFT4[13, 19, 20, 21, 22].”
Rigid supersymmetric theories in curved superspace (2011, methodology): “This fact has allowed [23,24,26-34] to compute Z”
The geometry of supersymmetric partition functions (2013, background): “Explicit computations of the index lead to a family of special functions that have recently been studied in the mathematical literature, see for instance [34–39] and references therein.”
SQCD: A Geometric Apercu (2008, background): “, [24, 25, 34, 22, 16, 37, 38, 18, 21, 35, 36, 39]) that count the number of BPS GIOs in various gauge theories.”
Reducing the 4d index to the S3 partition function (2011, methodology): “Hyper-multiplet As was first observed in [5], the index of the hypermultiplet can be written elegantly in terms of a special function [8] I = ∏”
The complete superconformal index for N=6 Chern–Simons theory (2009, background): “analysis of finite N indices for a class of 4 dimensional SCFT was reported in [50, 48].”