Generalized Superconformal Index for Three Dimensional Field Theories

By A. Kapustin, Brian Willett. 2011

198 citations recorded by the source corpus.

We introduce a generalization of the S^2 × S^1 superconformal index where background gauge fields with magnetic flux are coupled to the global symmetries of the theory. This allows one to gauge a global symmetry at the level of the index, which we use to show the matching of the superconformal index for N = 2 SQED with N_f flavors and its mirror dual.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/a5db79e1a703028af7e58e2d09cebc20e2f6eed7

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Citations in the corpus

Partition Functions of $${\mathcal{N}=(2,2)}$$N=(2,2) Gauge Theories on S2 and Vortices (2012, background): “A similar role is being played by the S3 and S2 × S1 partition functions [57,58], hence one could expect our result on S2 to fit into the pattern.”
The geometry of supersymmetric partition functions (2013, background): “As in four dimensions, a suitable trace over states on S(2) in Hamiltonian quantization defines a supersymmetric index I(y, u), where y and u are (generally complex) fugacities that couple to the Hamiltonian H, which generates translations along R, and an Abelian flavor charge Qf that commutes with ”
Comments on 3d Seiberg-like dualities (2011, background): “In particular the global Chern-Simons terms will be important when dealing with the generalized superconformal index recently proposed in [65].”
3-Manifolds and 3d Indices (2011, methodology): “ 0;q;0) = X m2Z I d 2ˇi 0mm0I T(m;q;); (2.13) with the integration done, as usual, on the unit circle. In this form, it is easier to see that the transformations agree with the general rules of [15,17] for gauging avor symmetries and adding Chern-Simons terms to the index. 6Note that the Sp(2N;Z) tr”
Bootstrapping the superconformal index with surface defects (2012, methodology): “s in 4dN= 2 theories on S4 [3], partition functions of 3dN= 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, 11, 12, 13, 14] (the latter are usually referred to as \superconformal indices" if the ”