Abstract
We construct a set of supersymmetric geometries that represent regular microstates of the D1-D5-P 3-charge system, using the solution generating technique of hep-th/0311092. These solutions are constructed as perturbations around the maximally rotating D1-D5 solution at the linear order, and depend on the coordinate of S^1 on which the D1- and D5-branes are wrapped. In the framework of six-dimensional supergravity developed by Gutowski, Martelli and Reall [hep-th/0306235], these solutions have a 4-dimensional base that depend on the S^1 coordinate v. The v-dependent base is expected of the superstratum solutions which are parametrized by arbitrary surfaces, and these solutions give a modest step toward their explicit construction.
Highlights
Is obtained by compactifying type IIB string theory on S1 ×M4 with M4 = T 4 or K3, wrapping N1 D1-branes on S1 and N5 D5-branes on S1×M4, and putting Np units of momentum along S1
We construct a set of supersymmetric geometries that represent regular microstates of the D1-D5-P 3-charge system, using the solution generating technique of [1]
It has been shown that the v-independent solutions are insufficient to account for the entropy of the D1-D5-P black hole [20]
Summary
We review the supersymmetric solutions in 6D supergravity as presented in [29]. We will be brief here; for more details the reader is referred to [2, 28, 29]. The most general supersymmetric solutions for this theory have a null Killing direction u, of which all fields are independent. Because null Killing vector introduces a 2 + 4 split in the geometry, it is natural to introduce a second retarded time coordinate v and a four-dimensional, and generically v-dependent, spatial base B with coordinates xm, m = 1, . Given the base B and the 1-form β satisfying the above equations, we can determine. . .] of G in (2.12) corresponds to D1(u, v) and the function Z1 is the potential for it. Inside B, D5(u, ψ, M4) is a 1-brane along ψ√and we can measure its charge by integrating Θ1 over a 2-surface going around it. Βm, ωm correspond to linear combinations of momentum charge along xm and KK monopole charge along xm × M4 with special circle v
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