On the higher-spin spectrum in large N Chern-Simons vector models

107

We propose a new approach to solve conformal field theories and apply it to Chern-Simons Matter theories and three-dimensional bosonization duality. All three-point correlation functions of single-trace operators are obtained in the large-N as a simple application. The idea is to construct, as an effective theory, a nonlinear realization of the conformal algebra in terms of physical, gauge-invariant, operators. The efficiency of the method is also in the use of an analog of the light-cone gauge and of the momentumspace on the CFT side. AdS/CFT is used as a convenient regulator and as a source of the canonical bracket. The uniqueness of the nonlinear realization manifests the threedimensional bosonization duality at this order. We also find two more non-unitary solutions which should be analogous to the fishnet theories. The results can also be viewed as an explicit realization of the slightly-broken higher spin symmetry.As a by-product, the cubic action of the Higher Spin Gravity in AdS 4 is constructed.While generic Higher Spin Gravities are obstructed at higher orders by nonlocality, we point out the existence of two especially simple and well-defined theories: chiral and anti-chiral whose three-point functions correspond to the two new solutions. These two theories are supposed to give a quantum complete and local example of gravitational bulk duals.

Section: Introduction and Main Resultsmentioning

confidence: 99%

Light-front bootstrap for Chern-Simons matter theories

Skvortsov

2019

107

“…Analytic progress, with this as the starting point, has been limited [28,29,[35][36][37][38][39][40]. In cases with weakly broken higher spin symmetry, some progress has been made in understanding the leading order anomalous dimensions [48][49][50] for lower spin operators as well -however, it is not clear how to systematize this approach to get subleading orders. The double light cone limit of the bootstrap equations in the works of [51][52][53][54] gives a systematic approach for the large spin limit.…”

Section: Introduction and Summary Of Resultsmentioning

confidence: 99%

Mellin space bootstrap for global symmetry

Dey

Kaviraj

Sinha

2017

121

We apply analytic conformal bootstrap ideas in Mellin space to conformal field theories with O(N ) symmetry and cubic anisotropy. We write down the conditions arising from the consistency between the operator product expansion and crossing symmetry in Mellin space. We solve the constraint equations to compute the anomalous dimension and the OPE coefficients of all operators quadratic in the fields in the epsilon expansion. We reproduce known results and derive new results up to O( 3 ). For the O(N ) case, we also study the large N limit in general dimensions and reproduce known results at the leading order in 1/N .

“…This approach was further generalized to extract leading order anomalous dimensions for other theories in [57][58][59][60]. Results have also been obtained at leading order (both for the -expansion as well as 1/N expansion) for anomalous dimensions of almost conserved higher spin currents [61][62][63]. These results crucially rely on the use of the equations of motion or a higher spin symmetry, that is present when the coupling constant goes to zero.…”

Section: Jhep05(2017)027mentioning

confidence: 99%

A Mellin space approach to the conformal bootstrap

Gopakumar

Kaviraj

Sen

et al. 2017

171

285

We describe in more detail our approach to the conformal bootstrap which uses the Mellin representation of CF T d four point functions and expands them in terms of crossing symmetric combinations of AdS d+1 Witten exchange functions. We consider arbitrary external scalar operators and set up the conditions for consistency with the operator product expansion. Namely, we demand cancellation of spurious powers (of the cross ratios, in position space) which translate into spurious poles in Mellin space. We discuss two contexts in which we can immediately apply this method by imposing the simplest set of constraint equations. The first is the epsilon expansion. We mostly focus on the Wilson-Fisher fixed point as studied in an epsilon expansion about d = 4. We reproduce Feynman diagram results for operator dimensions to O( 3 ) rather straightforwardly. This approach also yields new analytic predictions for OPE coefficients to the same order which fit nicely with recent numerical estimates for the Ising model (at = 1). We will also mention some leading order results for scalar theories near three and six dimensions. The second context is a large spin expansion, in any dimension, where we are able to reproduce and go a bit beyond some of the results recently obtained using the (double) light cone expansion. We also have a preliminary discussion about numerical implementation of the above bootstrap scheme in the absence of a small parameter.