Partial Spectral Flow in the D1D5 CFT

TL;DR

This paper investigates partial spectral flow in the D1D5 CFT, revealing how it affects the spectrum and energy lifts of states, especially when the theory is deformed away from the free point.

Contribution

It introduces the concept of partial spectral flow in the D1D5 CFT and analyzes its impact on the spectrum and state lifts under deformation.

Findings

Partial spectral flow can be used to study deformations away from the free point.

D1D5P states related by partial spectral flow generally have different energy lifts.

The transformation of the deformation under partial spectral flow is well-defined.

Abstract

The two-dimensional $\mathcal{N}=4$ superconformal algebra has a free field realization with four bosons and four fermions. There is an automorphism of the algebra called spectral flow. Under spectral flow, the four fermions are transformed together. In this paper, we study {\it partial spectral flow} where only two of the four fermions are transformed. Partial spectral flow is applied to the D1D5 CFT where a marginal deformation moves the CFT away from the free point. The partial spectral flow is broken by the deformation. We show that this effect can be studied due to a transformation of the deformation which is well-defined under partial spectral flow. As a result in the spectrum, we demonstrate how to compute the second-order energy lift of D1D5P states from their partial spectral flowed states. We find that D1D5P states related by partial spectral flow do not have the same lift in general.