d = 3 bosonic vector models coupled to Chern-Simons gauge theories

Abstract

We study three dimensional O(N ) k and U (N ) k Chern-Simons theories coupled to a scalar field in the fundamental representation, in the large N limit. For infinite k this is just the singlet sector of the O(N ) (U (N )) vector model, which is conjectured to be dual to Vasiliev's higher spin gravity theory on AdS 4 . For large k and N we obtain a parity-breaking deformation of this theory, controlled by the 't Hooft coupling λ = 4πN/k. For infinite N we argue (and show explicitly at two-loop order) that the theories with finite λ are conformally invariant, and also have an exactly marginal (φ 2 ) 3 deformation. For large but finite N and small 't Hooft coupling λ, we show that there is still a line of fixed points parameterized by the 't Hooft coupling λ. We show that, at infinite N , the interacting non-parity-invariant theory with finite λ has the same spectrum of primary operators as the free theory, consisting of an infinite tower of conserved higher-spin currents and a scalar operator with scaling dimension ∆ = 1; however, the correlation functions of these operators do depend on λ. Our results suggest that there should exist a family of higher spin gravity theories, parameterized by λ, and continuously connected to Vasiliev's theory. For finite N the higher spin currents are not conserved.

A minimal BV action for Vasiliev’s four-dimensional higher spin gravity

“…Besides the gauge-fixing procedure, which may require non-minimal sectors containing ghost-momenta and Nakanishi-Laudrup auxiliary fields, there are several lines of developments that present themselves at the present stage of which some are: [57,58,59,60]. In the latter respect, the four-form proposed by [51], that is, the quantity V (2) [4] given in Eq.…”

A master bosonization duality

“…They are crucial actors in mapping out the phase diagram of QCD 3 as well as some of its cousins. At large N, k, with N/k finite, they are dual to a peculiar theory of gravity known as Vasiliev theory [4][5][6]. These theories are in fact solvable in this limit, and much is known of their thermal physics and scattering amplitudes [4][5][6][19][20][21].…”

“…At large N, k, with N/k finite, they are dual to a peculiar theory of gravity known as Vasiliev theory [4][5][6]. These theories are in fact solvable in this limit, and much is known of their thermal physics and scattering amplitudes [4][5][6][19][20][21]. Away from N = k = N f = 1, they imply a web of dualities for gauge theories with product gauge groups and (bi)fundamental matter [22], known as quiver gauge theories, and have been embedded intro string theory [23] (see also [24]).…”

“…We find it useful to realize the SU(N ) theories as U(N ) × U(1) theories. 4 First, begin with U(N ) …”

“…There has been an accumulation of evidence this decade for dualities between nonsupersymmetric Chern-Simons theories coupled to fundamental matter [4][5][6][7][8]. These conjectured dualities may be thought of as taking the level/rank dualities, adding suitable matter content on both sides, and tuning to a conformal field theory (CFT).…”