Intertwining Relations for the Deformed D1D5 CFT

TL;DR

This paper introduces a new method using intertwining relations to analyze how deformation operators affect the D1D5 conformal field theory, aiding understanding of its moduli space and potential implications for black hole physics.

Contribution

It develops a novel, more direct computational approach for studying the effects of deformation operators on the D1D5 CFT, especially in the context of its orbifold point.

Findings

Derived intertwining relations for operator transformations

Provided a computational framework for single deformation effects

Potential applications to black hole microstate analysis

Abstract

The Higgs branch of the D1D5 system flows in the infrared to a two-dimensional N=(4,4) SCFT. This system is believed to have an "orbifold point" in its moduli space where the SCFT is a free sigma model with target space the symmetric product of copies of four-tori; however, at the orbifold point gravity is strongly coupled and to reach the supergravity point one needs to turn on the four exactly marginal deformations corresponding to the blow-up modes of the orbifold SCFT. Recently, technology has been developed for studying these deformations and perturbing the D1D5 CFT off its orbifold point. We present a new method for computing the general effect of a single application of the deformation operators. The method takes the form of intertwining relations that map operators in the untwisted sector before application of the deformation operator to operators in the 2-twisted sector after the application of the deformation operator. This method is computationally more direct, and may be of theoretical interest. This line of inquiry should ultimately have relevance for black hole physics.