Lifting of level-1 states in the D1D5 CFT

TL;DR

This paper investigates how certain supersymmetric states in the D1D5 conformal field theory lift in energy when moving away from the free orbifold point, providing detailed calculations for specific states at energy level 1.

Contribution

It offers a detailed analysis of the lifting pattern of level-1 states in the D1D5 CFT, including explicit second-order perturbation calculations for a specific set of states.

Findings

Identified 2688 states at energy level 1 in the D1D5 CFT.

Lifted states form a triplet of long multiplets with calculable energy shifts.

Half of the long multiplet members are in the untwisted sector, half in the twisted sector.

Abstract

The D1D5 CFT has a large set of states that are supersymmetric at the `free' orbifold point in moduli space. When we perturb away from this point, some of these states join into long multiplets and lift in energy, while others remain supersymmetric. The count of unlifted states can be bounded below by an index, but the index does not yield the pattern of lifting; i.e., which states join into a long multiplet and how much this multiplet lifts. In this paper we consider the simple case of the D1D5 CFT where the orbifold CFT is a sigma model with targets space $(T^4)^2/S_2$ and consider states at energy level $1$. There are $2688$ states at this level. The lifted states form a triplet of long multiplets, and we compute their lift at second order in perturbation theory. Half the members of the long multiplet are in the untwisted sector and half are in the twisted sector. This and other similar studies should help in the understanding of fuzzball states that describe extremal holes, since CFT sectors with low twist describe shallow throats in the dual gravity solution while sectors with high twist describe deep throats.