Holographic anatomy of fuzzballs

TL;DR

This work advances the holographic understanding of 2-charge fuzzballs by linking each horizon-free D1-D5 geometry—sourced by a curve in R^4—to a specific superposition of R-ground states through a coherent-state map of FP perturbations. The authors develop a non-linear KK reduction and gauge-invariant fluctuation formalism to extract vevs of chiral primaries, currents, and the stress tensor, finding precise kinematical matches and partial dynamical agreement at leading supergravity. They demonstrate that generic fuzzball geometries correspond to superpositions of R-ground states, with elliptic and circular examples providing detailed tests; dynamical constraints, particularly multi-particle three-point functions at strong coupling, lie beyond the leading approximation. The paper also investigates symmetric (averaged) geometries and the inclusion of asymptotically flat regions, arguing that while the fuzzball program remains supported, the exact state-geometry map is intricate and generally requires going beyond the leading supergravity description to resolve fully. Overall, the results illuminate how geometric data encode boundary CFT vevs and charges, offering a framework to test microstate proposals via holography and AdS/CFT in the Higgs/C Coulomb contexts.

Abstract

We present a comprehensive analysis of 2-charge fuzzball solutions, that is, horizon-free non-singular solutions of IIB supergravity characterized by a curve on R^4. We propose a precise map that relates any given curve to a specific superposition of R ground states of the D1-D5 system. To test this proposal we compute the holographic 1-point functions associated with these solutions, namely the conserved charges and the vacuum expectation values of chiral primary operators of the boundary theory, and find perfect agreement within the approximations used. In particular, all kinematical constraints are satisfied and the proposal is compatible with dynamical constraints although detailed quantitative tests would require going beyond the leading supergravity approximation. We also discuss which geometries may be dual to a given R ground state. We present the general asymptotic form that such solutions must have and present exact solutions which have such asymptotics and therefore pass all kinematical constraints. Dynamical constraints would again require going beyond the leading supergravity approximation.