Superconformal indices of three-dimensional theories related by mirror symmetry

By Christian Krattenthaler, V. Spiridonov, G. Vartanov. 2011

133 citations recorded by the source corpus.

Recently, Kim, and Imamura and Yokoyama derived an exact formula for superconformal indices in three-dimensional field theories. Using their results, we prove analytically the equality of superconformal indices in some U(1)-gauge group theories related by mirror symmetry. The proofs are based on well-known identities in the theory of q-special functions. We also suggest a general index formula taking into account the U(1)J global symmetry present for abelian theories.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/07fe7c72b3e211ad57c7f212663ca33d8b54b5f2

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In Nuclear and High Energy Physics

Citations in the corpus

Comments on 3d Seiberg-like dualities (2011, background): “An important tool for that is the superconformal index [63, 64]: it would be nice to check that it matches between dual theories.”
3d dualities from 4d dualities (2013, background): “. |W|{m ℓ} is the symmetry factor in the given monopole sector, and α(m) are the roots of the gauge group G. 26 See [89] for a recent discussion of this issue in the context of the 3d index. See also [90,91,92]. For sign subtleties in the case of a 3d partition function on a Lens space see [93]. 71 ”
Exact results in D = 2 supersymmetric gauge theories (2012, unknown): “[6] in evaluating the partition function of three dimensional N = 2 abelian gauge theories on the squashed S3 [7] and S1 × S2.”
Partition Functions of $${\mathcal{N}=(2,2)}$$N=(2,2) Gauge Theories on S2 and Vortices (2012, background): “s a limit of a three-dimensional localized partition function on a suitable manifold.26 8.1 S2 ×S1 A natural guess is to consider the supersymmetric partition function of a 3d N = 2 theory on S2 × S1 [10, 57, 58], which computes a supersymmetric index of the theory, in the limit where the S1 shrinks”
N=2 supersymmetric theories on squashed three-sphere (2011, methodology): “The superconformal index is also used to check these dualities[19, 20, 21, 22, 13].”
Index for three dimensional superconformal field theories with general R-charge assignments (2011, background): “After completion of the revision, a paper appeared[20] which also studies the index with such chemical potentials for theories studied in Section 5.”
3-Manifolds and 3d Indices (2011, methodology): “In [16, 17] the match was also proven at special values of m = (m1,m2) using different methods.”
The gravity dual of supersymmetric gauge theories on a squashed three-sphere (2011, background): “The matching of partition functions also allows one to perform non-trivial tests of conjectured dualities between pairs of three-dimensional field theories [18, 19, 20, 21, 22, 23, 24, 25, 26].”
Bootstrapping the superconformal index with surface defects (2012, background): “Four important classes of examples are expectation values of circular Wilson loops in 4d N = 2 theories on S4 [3], partition functions of 3d N = 2 theories on S3 [4, 5, 6], partition functions of N = 1 and N = 2 theories on S3 × S1 [7, 8] and partition functions of N = 2 theories on S2 × S1 [9, 10, ”
Lectures on localization and matrix models in supersymmetric Chern–Simons-matter theories (2011, methodology): “They have also been used to compute supersymmetric indices in S2 × S1 [65, 53, 69] and to study CS-matter theories in other three-manifolds [49, 43, 59].”