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

Bhattacharya, Jyotirmoy; Bhattacharyya, Sayantani; Minwalla, Shiraz; Raju, Suvrat

doi:10.1088/1126-6708/2008/02/064

Cited by 261 publications

(465 citation statements)

References 38 publications

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“…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 Q f that commutes with the supercharges [75][76][77][78]. (As in four dimensions, generic values of the chemical potentials are only consistent with two supercharges.)…”

Section: S 2 × S 1 Without Flux and The Supersymmetric Indexmentioning

confidence: 99%

The geometry of supersymmetric partition functions

Closset

Dumitrescu

Festuccia

et al. 2014

J. High Energ. Phys.

167

415

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We consider supersymmetric field theories on compact manifolds M and obtain constraints on the parameter dependence of their partition functions Z M . Our primary focus is the dependence of Z M on the geometry of M, as well as background gauge fields that couple to continuous flavor symmetries. For N = 1 theories with a U(1) R symmetry in four dimensions, M must be a complex manifold with a Hermitian metric. We find that Z M is independent of the metric and depends holomorphically on the complex structure moduli. Background gauge fields define holomorphic vector bundles over M and Z M is a holomorphic function of the corresponding bundle moduli. We also carry out a parallel analysis for three-dimensional N = 2 theories with a U(1) R symmetry, where the necessary geometric structure on M is a transversely holomorphic foliation (THF) with a transversely Hermitian metric. Again, we find that Z M is independent of the metric and depends holomorphically on the moduli of the THF. We discuss several applications, including manifolds diffeomorphic to S 3 ×S 1 or S 2 ×S 1 , which are related to supersymmetric indices, and manifolds diffeomorphic to S 3 (squashed spheres). In examples where Z M has been calculated explicitly, our results explain many of its observed properties.

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Section: S 2 × S 1 Without Flux and The Supersymmetric Indexmentioning

confidence: 99%

The geometry of supersymmetric partition functions

Closset

Dumitrescu

Festuccia

et al. 2014

J. High Energ. Phys.

167

415

View full text Add to dashboard Cite

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“…Then one can reduce the Abelian theory along the circle to obtain a 5d theory, and calculate the partition function after a non-Abelian generalization which can be used to study the general superconformal index [16,17] of the 6d (2, 0) theory. This problem is studied in our later work [10].…”

Section: Motivation From Abelian Theoriesmentioning

confidence: 99%

M5-branes from gauge theories on the 5-sphere

Kim

2013

J. High Energ. Phys.

204

416

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We use the 5-sphere partition functions of supersymmetric Yang-Mills theories to explore the (2, 0) superconformal theory on S 5 × S 1 . The 5d theories can be regarded as Scherk-Schwarz reductions of the 6d theory along the circle. In a special limit, the perturbative partition function takes the form of the Chern-Simons partition function on S 3 . With a simple non-perturbative completion, it becomes a 6d index which captures the degeneracy of a sector of BPS states as well as the index version of the vacuum Casimir energy. The Casimir energy exhibits the N 3 scaling at large N . The large N index for U (N ) gauge group also completely agrees with the supergravity index on AdS 7 × S 4 .

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“…The full spectrum of short representations is encoded in the superconformal index up to cancellations between representations that can recombine (group theoretically) to form a long representation [95]. The allowed recombinations are reviewed in Appendix A.…”

Section: General Short Representations and The Superconformal Indexmentioning

confidence: 99%

“…We recall the classification of unitarity irreducible representations of the ospð8 ⋆ j4Þ superalgebra. These have been described in [91,95,120] and are reviewed in [50]. There are four linear relations at the level of quantum numbers that, if satisfied by the superconformal primary state in a representation, guarantee that the resulting representation is (semi)short.…”

Section: Acknowledgmentsmentioning

confidence: 99%

The (2, 0) superconformal bootstrap

et al. 2016

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We develop the conformal bootstrap program for six-dimensional conformal field theories with (2, 0) supersymmetry, focusing on the universal four-point function of stress tensor multiplets. We review the solution of the superconformal Ward identities and describe the superconformal block decomposition of this correlator. We apply numerical bootstrap techniques to derive bounds on operator product expansion (OPE) coefficients and scaling dimensions from the constraints of crossing symmetry and unitarity. We also derive analytic results for the large spin spectrum using the light cone expansion of the crossing equation. Our principal result is strong evidence that the A 1 theory realizes the minimal allowed central charge (c ¼ 25) for any interacting (2, 0) theory. This implies that the full stress tensor four-point function of the A 1 theory is the unique unitary solution to the crossing symmetry equation at c ¼ 25. For this theory, we estimate the scaling dimensions of the lightest unprotected operators appearing in the stress tensor operator product expansion. We also find rigorous upper bounds for dimensions and OPE coefficients for a general interacting (2, 0) theory of central charge c. For large c, our bounds appear to be saturated by the holographic predictions obtained from eleven-dimensional supergravity.

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

Cited by 261 publications

References 38 publications

The geometry of supersymmetric partition functions

The geometry of supersymmetric partition functions

M5-branes from gauge theories on the 5-sphere

The (2, 0) superconformal bootstrap

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