Abstract
We study two families of composite twisted Ramond fields (made by products of two operators) in the $\cal {N}=(4,4)$ supersymmetric D1-D5 SCFT$_2$ deformed by a marginal modulus operator away from its $(T^4)^N/ S_N$ free orbifold point. We construct the large-$N$ contributions to the four-point functions with two composite operators and two deformation fields. These functions allow us to derive short-distance OPE limits and to calculate the anomalous dimensions of the composite operators. We demonstrate that one can distinguish two sets of composite Ramond states with twists $m_1$ and $m_2$: protected states, for which $m_1+m_2=N$, and "lifted" states for which $m_1+m_2<N$. The latter require an appropriate renormalisation. We also derive the leading order corrections to their two-point functions, and to their three-point functions with the deformation operator.
Highlights
The scalar moduli deformation of the symmetric orbifold ðT4ÞN=SN gives rise to a particular two-dimensional N 1⁄4 ð4; 4Þ superconformal theory with central charge c 1⁄4 6N, which for large values of N provides a fuzzball [1] description of certain five-dimensional extremal supersymmetric black holes
Similar statements hold for the microstates of the more realistic near-extremal 3-charge 1=8-BPS black holes, the so-called D1-D5-P system, which can be realized as appropriate tensor products of the descendants of twisted
As we have demonstrated in a recent paper [27], the simplest R-charged twisted Ramond fields RÆn ðz; zÞ get renormalized, i.e., their conformal dimensions and certain structure constants acquire corrections in the perturbed theory
Summary
The scalar moduli deformation of the symmetric orbifold ðT4ÞN=SN gives rise to a particular two-dimensional N 1⁄4 ð4; 4Þ superconformal theory with central charge c 1⁄4 6N, which for large values of N provides a fuzzball [1] description of certain five-dimensional extremal supersymmetric black holes. Their type IIB superstring counterparts are bound states of the D1-D5 brane system (see, e.g., [2,3] for a more recent review), which gave the first microscopical account of the Bekenstein-Hawking entropy [4]. The remaining composite fields, with m1 þ m2 < N, suffer from certain UV divergences and do require an appropriate renormaliz þ ation; as a result, their conformal dimensions get corrected
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