Correlation functions of composite Ramond fields in deformed D1-D5 orbifold SCFT$_2$

TL;DR

This paper analyzes the behavior of composite Ramond fields in a deformed D1-D5 SCFT$_2$, calculating four-point functions, anomalous dimensions, and distinguishing protected from lifted states.

Contribution

It constructs large-$N$ four-point functions for composite operators in the deformed D1-D5 SCFT$_2$ and identifies criteria to distinguish protected and lifted Ramond states.

Findings

Identified protected states with $m_1+m_2=N$

Calculated anomalous dimensions of composite operators

Derived corrections to two- and three-point functions

Abstract

We study two families of composite twisted Ramond fields (made by products of two operators) in the $\cal {N}=(4,4)$ supersymmetric D1-D5 SCFT$_2$ deformed by a marginal modulus operator away from its $(T^4)^N/ S_N$ free orbifold point. We construct the large-$N$ contributions to the four-point functions with two composite operators and two deformation fields. These functions allow us to derive short-distance OPE limits and to calculate the anomalous dimensions of the composite operators. We demonstrate that one can distinguish two sets of composite Ramond states with twists $m_1$ and $m_2$: protected states, for which $m_1+m_2=N$, and "lifted" states for which $m_1+m_2<N$. The latter require an appropriate renormalisation. We also derive the leading order corrections to their two-point functions, and to their three-point functions with the deformation operator.