Colour-twist operators. Part I. Spectrum and wave functions

Andrea Cavaglià,David Grabner,Amit Sever,Nikolay Gromov

doi:10.1007/jhep06(2020)092

Abstract

We introduce a new class of operators in any theory with a ’t Hooft large-N limit that we call colour-twist operators. They are defined by twisting the colour-trace with a global symmetry transformation and are continuously linked to standard, untwisted single-trace operators. In particular, correlation functions between operators that are twisted by an R-symmetry of mathcal{N} = 4 SYM extend those in the γ-deformed theory. The most general deformation also breaks the Lorentz symmetry but preserves integrability in the examples we consider. In this paper, we focus on colour-twist operators in the fishnet model. We exemplify our approach for the simplest colour-twist operators with one and two scalar fields, which we study non-perturbatively using field-theoretical as well as integrability methods, finding a perfect match. We also propose the quantisation condition for the Baxter equation appearing in the integrability calculation in the fishnet model. The results of this paper constitute a crucial step towards building the separation of variable construction for the correlation functions by means of the Quantum Spectral Curve approach.

Highlights

Twist operators play an important role in two-dimensional conformal field theories
The results of this paper constitute a crucial step towards building the separation of variable construction for the correlation functions by means of the Quantum Spectral Curve approach
We have introduced a novel type of operators, which can be constructed in any theory with a ’t Hooft large-N limit by twisting the colour-trace: colour-twist operators

Summary

Introduction

Twist operators play an important role in two-dimensional conformal field theories. They are defined by the action of a symmetry as one goes around the operator [1,2,3]. We study a new type of twist operators in the ’t Hooft large-N limit that we call “colour-twist operators”. They may be defined as a generalisation of single-trace operators, where the colour-trace is accompanied by a symmetry transformation. In this picture, going around the operator takes place in colour space instead of spacetime. In holographic theories, we expect our field theory definition to coincide with twisted vertex operators in the two-dimensional worldsheet CFT of the dual string

Methods

Results

Conclusion