Indices for superconformal field theories in 3, 5 and 6 dimensions

By J. Bhattacharya, Sayantani Bhattacharyya, Shiraz Minwalla, S. Raju. Journal of High Energy Physics, 2008

328 citations recorded by the source corpus.

We present a trace formula for a Witten type Index for superconformal field theories in d = 3, 5 and 6 dimensions, generalizing a similar recent construction in d = 4. We perform a detailed study of the decomposition of long representations into sums of short representations at the unitarity bound to demonstrate that our trace formula yields the most general index (i.e. quantity that is guaranteed to be protected by superconformal symmetry alone) for the corresponding superalgebras. Using the dual gravitational description, we compute our index for the theory on the world volume of N M2 and M5 branes in the large N limit. We also compute our index for recently constructed Chern Simons theories in three dimensions in the large N limit, and find that, in certain cases, this index undergoes a large N phase transition as a function of chemical potentials.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/e54308538ed14414e6a8885a5619d7a40dcb9a44

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Citations in the corpus

Exact correlators of BPS Operators from the 3d superconformal bootstrap (2014, background): “For any N = 2 SCFT one can define the superconformal index [68,71] as”
Index for three dimensional superconformal field theories with general R-charge assignments (2011, methodology): “Such an analysis is performed in [8, 9, 11] for the ABJM model and the complete agreement of the gauge theory index and the gravity index is confirmed.”
Deformations of superconformal theories (2016, methodology): “(See [12, 19, 23] and references therein for a more detailed discussion.”
Framed BPS states (2010, unknown): “1 Chiral primary fields The DLCQ definition of the Ar theories shows that there are local chiral primary fields generating short multiplets of the superconformal algebra [51, 52].”
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 ”
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.”
The complete superconformal index for N=6 Chern–Simons theory (2009, background): “The general structure of the superconformal index was investigated in 4 dimension [2], and then in 3, 5, 6 dimensions [3].”
5-dim superconformal index with enhanced En global symmetry (2012, unknown): “The commutator of Qm and S m A reads [18, 19] {Qm, S B} = δ m δ BD + 2 δ BMm − 3 δ mRB , (2.”
4d Index to 3d Index and 2d TQFT (2011, background): “Recent studies have uncovered powerful techniques (mostly based on localization) to extract exact results for 3d and 4d supersymmetric gauge theories, including the 4d N ≥ 1 superconformal index on S(1) × S(3) [1, 2], the 4d N ≥ 2 partition function on S(4) [3], the 3d N ≥ 2 partition function on S(”