Index for three dimensional superconformal field theories with general R-charge assignments

By Y. Imamura, Shuichiro Yokoyama. 2011

358 citations recorded by the source corpus.

We derive a general formula of an index for three dimensional $ \mathcal{N} = 2 $ super-conformal field theories with general R-charge assignments to chiral multiplets by using the localization method in S2 × S1 background. As examples we compute the index for theories in a few mirror pairs, and confirm the agreement of the indices in each mirror pair.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/bf254d40379028f70de19ec95a07c2163f65d89e

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In Nuclear and High Energy Physics

Citations in the corpus

M5-branes from gauge theories on the 5-sphere (2012, neutral): “For non-canonical R-charges with 3d N = 2 SUSY, one finds a factor [59] f(x) = xh − x2−h 1− x2 (B.”
N=2 supersymmetric theories on squashed three-sphere (2011, background): “In the case of three dimensional theories, the superconformal index[1, 2, 3] and S(3) partition function[4, 5, 6] are such calculable quantities.”
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].”
SUSY gauge theories on squashed three-spheres (2011, background): “It has recently been generalized to arbitrary N = 2 supersymmetric gauge theories by [12].”
Partition Functions of $${\mathcal{N}=(2,2)}$$N=(2,2) Gauge Theories on S2 and Vortices (2012, methodology): “A longer version of this paper is available online [25], where we present more examples, some consistency checks with mirror symmetry, and a comparison with the threedimensional matrix integral for lens spaces L(p, 1) [13,15] in the p → ∞ limit, and with the three-dimensional integral for the index ”
The geometry of supersymmetric partition functions (2013, background): “Any N = 2 theory with a U(1)R symmetry can be placed on S 2 × R with the usual round metric while preserving four supercharges residing in SU(2|1), which contains the SU(2) isometry of the sphere [75].”
Exact results in D = 2 supersymmetric gauge theories (2012, neutral): “(3.28) It is worth mentioning that these field configurations are also supersymmetric configurations in the localization computation of the partition function of three dimensional N = 2 gauge theories on S1×S2 [12], which computes the superconformal index of these theories.”
A topologically twisted index for three-dimensional supersymmetric theories (2015, background): “As first observed in [14] and later elaborated upon in [15, 16], both the S3 partition function of [29], the S2×S1 supersymmetric index of [47, 48] and the lens space index of [49] “factorize” into building elements which can be interpreted as the partition function on R(2)Ω×S(1) in an Ω-background.”
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, ”
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.”
Supersymmetric field theories on three-manifolds (2012, methodology): “Following [1-4], much work has focused on supersymmetric theories on round and squashed spheres [5-13].”
Localization techniques in quantum field theories (2016, methodology): “Surprisingly, the first derivative of the imaginary part ImF need not vanish, due to a global superconformal anomaly that can arise in three dimensions [39,40].”
4d Index to 3d Index and 2d TQFT (2011, background): “This result coincides with the formula for the 3d index given in [11],(7) 8 provided that we identify x = t(3).”