The complete superconformal index for N=6 Chern–Simons theory

By Seok Kim. 2009

433 citations recorded by the source corpus.

Abstract We calculate the superconformal index for N = 6 Chern–Simons-matter theory with gauge group U ( N ) k × U ( N ) − k at arbitrary allowed value of the Chern–Simons level k . The calculation is based on localization of the path integral for the index. Our index counts supersymmetric gauge invariant operators containing inclusions of magnetic monopole operators, where latter operators create magnetic fluxes on 2-sphere. Through analytic and numerical calculations in various sectors, we show that our result perfectly agrees with the index over supersymmetric gravitons in AdS 4 × S 7 / Z k in the large N limit. Monopole operators in nontrivial representations of U ( N ) × U ( N ) play important roles. We also comment on possible applications of our methods to other superconformal Chern–Simons theories.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/8b2bc8a7ee2a81eda1b63dbbefde6dc1bbf9d73c

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Citations in the corpus

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.”
Exact correlators of BPS Operators from the 3d superconformal bootstrap (2014, methodology): “The superconformal index of U(N)k × U(Ñ)−k ABJ(M) theory can be computed using supersymmetric localization following, for instance, [72–75].”
Localization techniques in quantum field theories (2016, methodology): “Due to some powerful non-renormalization theorems [24,38], this formula for the Kähler potential on Mc is not subject to quantum corrections.”
5-dim superconformal index with enhanced En global symmetry (2012, neutral): “3 of [29].”
Microscopic origin of the Bekenstein-Hawking entropy of supersymmetric AdS5 black holes (2018, methodology): “ial rescaling), Kis the same supersymmetric Killing vector (2.17) of the bulk solution, just expressed in dierent coordinates dened in (3.49).9 The action 9This is equivalent to the prescription of [56] which exchanges twisted boundary conditions along time circle for dynamical elds for periodic bou”
3d dualities from 4d dualities (2013, methodology): “ontext 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 The main diﬀerence between (A.3) and the prescription discussed in [87,88,85] is that diﬀerent magnetic sectors are weighed with diﬀerent signs. In a generic duality, ”
Numerical studies of the ABJM theory for arbitrary N at arbitrary coupling constant (2012, positive): “urther. 1This formula is also reproduced by a numerical simulation in the large-N limit [17, 18]. 2The localization of the ABJM theory and related theories on various manifolds such as S3 [24], 1 × 2 [25] and squashed S3 [26] has also been considered. – 3 – In this paper we show that the ABJM matrix”
M5-branes from gauge theories on the 5-sphere (2012, methodology): “2), one finds that [40] ǫ0 = 1 2 lim x→1− x d dx f(x) , (B.”
Lectures on localization and matrix models in supersymmetric Chern–Simons-matter theories (2011, positive): “metric gauge theories [62, 63, 57, 60, 96], by showing that their partition functions agree as functions of the various parameters. They have also been used to compute supersymmetric indices in S2 S1 [65, 53, 69] and to study Chern{Simons{matter theories in other three-manifolds [49, 43, 59]. In con”
FROM 4d SUPERCONFORMAL INDICES TO 3d PARTITION FUNCTIONS (2011, background): “SCIs of 3d field theories have an essentially more involved form (due to monopole contributions, that do not analogously arise for 4d theories) – see [8, 9, 10, 11, 12] and references therein.”
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, ”
Index for three dimensional superconformal field theories with general R-charge assignments (2011, methodology): “The reader should refer to [11] for details about the contribution of vector multiplets.”
The exact superconformal R-symmetry extremizes Z (2010, background): “Moreover the resulting answers can be written in closed form, unlike the perhaps richer invariants given by the superconformal index on S(2) × S(1) studied in [23].”
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 [30], the S2 × S1 supersymmetric index of [51, 52] and the lens space index of [53] “factorize” into building elements which can be interpreted as the partition function on R(2)Ω ×S1 in an Ω-background”
4d Index to 3d Index and 2d TQFT (2011, background): “where we remove the divergent part in the β → 0 limit [10, 11].”