Dynamics of R-neutral Ramond fields in the D1-D5 SCFT

TL;DR

This paper investigates how marginal deformations affect R-neutral Ramond fields in the D1-D5 superconformal field theory, analyzing their dynamics, correlation functions, and renormalization properties in the large-N limit.

Contribution

It provides an explicit analytic computation of four-point functions involving R-neutral Ramond fields under deformation, revealing their scaling dimensions and renormalization behavior.

Findings

Two approaches yield consistent four-point functions.

Non-BPS fields acquire finite anomalous dimensions after renormalization.

Maximal twist fields remain protected from renormalization.

Abstract

We describe the effect of the marginal deformation of the $\cal N = (4, 4)$ superconformal $(T^4)^N /S_N$ orbifold theory on a doublet of R-neutral twisted Ramond fields, in the large-$N$ approximation. Our analysis of their dynamics explores the explicit analytic form of the genus-zero four-point function involving two R-neutral Ramond fields and two deformation operators. We compute this correlation function with two different approaches: the Lunin-Mathur path-integral technique and the stress-tensor method. From its short distance limits, we extract the OPE structure constants and the scaling dimensions of non-BPS fields appearing in the fusion. In the deformed CFT, at second order in the deformation parameter, the two-point function of the $n$-twisted Ramond fields is UV-divergent. We perform an appropriate regularization, together with a renormalization of the undeformed fields, obtaining finite, well-defined corrections to their two-point functions and their bare conformal weights, for $n < N$. The fields with maximal twist $n=N$ remain protected from renormalization, with vanishing anomalous dimensions.