Complete factorization in minimal N = 4 $$ \mathcal{N}=4 $$ Chern-Simons-matter theory

Abstract

Abstract:We investigate an N = 4 U(N ) k × U(N + M ) −k Chern-Simons theory coupled to one bifundamental hypermultiplet by employing its partition function, which is given by 2N + M dimensional integration via localization. Surprisingly, by performing the integration explicitly we find that the partition function completely factorizes into that of the pure Chern-Simons theory for two gauge groups and an analogous contribution for the bifundamental hypermultiplet. Using the factorized form of the partition function we argue the level/rank duality, which is also expected from the Hanany-Witten transition in the type IIB brane realization. We also present the all order 't Hooft expansion of the partition function and comment on the connection to the higher-spin theory.

Bose-Fermi Chern-Simons dualities in the Higgsed phase

“…2 See [12-15] for more precise versions of the duality map. 3 See [5,9,10,16,17,20,[23][24][25][33][34][35][36][37][38][39][40][41][42][43][44][45][46] for other large-N computations that provide additional evidence for this duality.…”

Supersymmetry breaking in a large N gauge theory with gravity dual

“…Naively, for M = 0 this theory can be obtained by taking the decoupling limit ζ 2 → ∞ in the mass deformed ABJM theory. Indeed we observe for N < k/2 that, if we take the limit ζ 2 → ∞ in the exact expressions for the partition function Z(N, k, 0, ζ 2 ) they precisely coincide with those in [16] up to the contribution of decoupled hypermultiplet e −2πN 2 ζ 2 /k (see app. C.2).…”

“…Although we explicitly present only the four cases, we have observed similar behaviors for various other values of (k, ζ 1 , ζ 2 ) satisfying ζ 1 ζ 2 k 2 < 1 16 . Figure 5 shows similar plots for ζ 1 ζ 2 k 2 ≥ 1 16 where we expect that we cannot trust (5.21) due to the correction (5.23). In contrast to fig.…”

“…1. We expect that the partition function vanishes when ζ 1 ζ 2 k 2 = 1 16 and the theory is in the SUSY breaking phase for ζ 1 ζ 2 k 2 ≥ 1 16 . In sec.…”

“…Figure 1: Our proposal on phase structure of the massive ABJM theory on S 3 in the large-N limit. The dashed line denotes expected zeroes of the sphere partition function: ζ 1 ζ 2 k 2 = 1 16 .…”