Field Theory of Primaries in W_N Minimal Models

TL;DR

This paper develops a nonlinear field theory for primary operators in large N W_N minimal model CFTs, capturing their spectrum and interactions, and relates it to matrix-vector models.

Contribution

It introduces a novel nonlinear field theory framework for primaries in W_N models, explicitly reproducing their spectrum and connecting to matrix-vector models.

Findings

Constructed a Hamiltonian matching conformal dimensions

Formulated a nonlinear field theory with cubic and quartic interactions

Linked the theory to matrix-vector models

Abstract

For W_N minimal model CFT's at Large N, we formulate a nonlinear field theory of primary operators. A classification of single-trace operators is given first based on which an interacting field theory operating in Fock space is built. A hamiltonian is constructed with the property that it reproduces exactly the spectrum of conformal dimensions of all the primaries. This field theory is characterized by cubic (and quartic) interactions with G=1/N as an interaction parameter. It is seen that the 1/N nonlinear representation contains the interactions and structure known from Matrix-vector models.