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 (T4)2/S2 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.
Highlights
The D1D5P system provides a very useful instance of an extremal black hole in string theory [1,2,3,4]
The lifted states form a triplet of long multiplets, and we compute their lift at second order in perturbation theory
Such states correspond to microstates of the extremal black hole, and preserve 1/8 of the supersymmetries of the string theory
Summary
The D1D5P system provides a very useful instance of an extremal black hole in string theory [1,2,3,4]. Sets of extremal states can join up into larger multiplets and lift to higher energies, leaving a smaller set of states that remain extremal The latter set is the set of microstates of the extremal black hole. On the other hand we know from the index computation of [13] that if we go to sufficiently high energies and twists to describe black hole states, a large number of states must remain unlifted : the index of [13] agrees with the Bekenstein entropy of extremal holes for large charges. We consider the lowest nontrivial amount of momentum charge: P = 1 Even with these choices, the number of extremal states at this level in the orbifold CFT is 2688, which is a largish number. For more computations in conformal perturbation theory in two and higher dimensional CFTs see, e.g. [35,36,37,38,39,40,41,42,43,44,45,46,47]
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