Renormalization of Twisted Ramond Fields in D1-D5 SCFT$_2$

TL;DR

This paper investigates the renormalization of twisted Ramond fields in the D1-D5 superconformal field theory, deriving corrections to conformal dimensions and structure constants through large-N analysis and addressing UV divergences.

Contribution

It provides the first detailed calculation of field renormalization and conformal dimension corrections for Ramond fields in the deformed D1-D5 SCFT at large N.

Findings

Calculated the large-N limit of four-point functions involving Ramond fields.

Identified UV divergences in second-order corrections and performed renormalization.

Derived corrections to conformal dimensions and structure constants of Ramond states.

Abstract

We explore the Ramond sector of the deformed two-dimensional $\cal N = (4, 4)$ superconformal $(T^4)^N /S_N$ orbifold theory, describing bound states of D1-D5 brane system in type IIB superstring. We derive the large-$N$ limit of the four-point function of two R-charged twisted Ramond fields and two marginal deformation operators at the free orbifold point. Specific short-distance limits of this function provide several structure constants, the OPE fusion rules and the conformal dimensions of a few non-BPS operators. The second order correction (in the deformation parameter) to the two-point function of the Ramond fields, defined as double integrals over this four-point function, turns out to be UV-divergent, requiring an appropriate renormalization of the fields. We calculate the corrections to the conformal dimensions of the twisted Ramond ground states at the large-$N$ limit. The same integral yields the first-order deviation from zero of the structure constant of the three-point function of two Ramond fields and one deformation operator. Similar results concerning the correction to the two-point function of bare twist operators and their renormalization are also obtained.