Absorption and Hawking Radiation of Minimal and Fixed Scalars, and AdS/CFT correspondence

TL;DR

This work provides a complete ab initio derivation of absorption cross-sections and Hawking radiation for minimal and fixed scalars in the five-dimensional D1-D5 black hole, beginning from the D1-D5 moduli space and invoking the AdS/CFT correspondence to fix bulk–brane couplings. It identifies the correct SCFT operators that couple to bulk fields by exploiting near-horizon symmetry and confirms, through both SCFT and supergravity calculations, that the two-point functions agree when the normalization is set to $\mu=1$, while the three-point functions vanish in either framework, reflecting nonrenormalization and holomorphic factorization. The fixed-scalar problem is resolved by showing only $(h,\bar h)=(2,2)$ operators can couple, eliminating prior discrepancies with semiclassical results. Collectively, the results reinforce the AdS/CFT paradigm by linking large-$N$ gauge dynamics to bulk gravity on $AdS_3\times S^3\times T^4$ and demonstrate a quantitative mechanism for translating D-brane data into gravitational observables.

Abstract

We present a complete derivation of absorption cross-section and Hawking radiation of minimal and fixed scalars from the Strominger-Vafa model of five-dimensional black hole, starting right from the moduli space of the D1-D5 brane system. We determine the precise coupling of this moduli space to bulk modes by using the AdS/CFT correspondence. Our methods resolve a long-standing problem regarding emission of fixed scalars. We calculate three-point correlators of operators coupling to the minimal scalars from supergravity and from SCFT, and show that both vanish. We make some observations about how the AdS/SYM correspondence implies a close relation between large $N$ equations of motion of $d$-dimensional gauge theory and supergravity equations on $AdS_{d+1}$-type backgrounds. We compare with the explicit nonlocal transform relating 1 and 2 dimensions in the context of $c=1$ matrix model.