Emission from the D1D5 CFT

TL;DR

This work builds a concrete bridge between the D1D5 CFT at the orbifold point and its gravity dual by formulating how flat-space fields couple to the CFT and by constructing explicit vertex operators for minimally coupled supergravity scalars. Using spectral flow, the authors map between Ramond and NS sectors to simplify calculations, then compute CFT amplitudes for emission from simple and highly excited states, including nonextremal microstates. They derive the emission rate formulas, perform careful combinatorics over the orbifold copies, and demonstrate exact agreement with gravity predictions in the dual geometry, reinforcing the AdS/CFT correspondence for dynamical emission processes. The framework is then extended to nonextremal states, showing Bose-enhancement in the emission rate and linking the CFT results to Hawking-like radiation from corresponding microstates. The methodology provides a robust toolkit for computing a wide class of CFT emission amplitudes and paves the way for exploring deformations away from the orbifold point. Overall, the paper solidifies the microscopic CFT description of D1D5 radiation and exemplifies precise matches with gravity across extremal and nonextremal regimes.

Abstract

It is believed that the D1D5 brane system is described by an 'orbifold CFT' at a special point in moduli space. We first develop a general formulation relating amplitudes in a d-dimensional CFT to absorption/emission of quanta from flat infinity. We then construct the D1D5 vertex operators for minimally coupled scalars in supergravity, and use these to compute the CFT amplitude for emission from a state carrying a single excitation. Using spectral flow we relate this process to one where we have emission from a highly excited initial state. In each case the radiation rate is found to agree with the radiation found in the gravity dual.

Figures (6)

• Figure 1: (a) The geometry of branes is flat at infinity, then we have a 'neck', and further in the geometry takes the form $AdS_{d+1}\times S^p$ (b) Still further in, the geometry ends in a 'fuzzball cap' whose structure is determined by the choice of microstate. For the simple state that we will choose for the D1D5 system, the Cap+AdS region is just a part of global $AdS$.
• Figure 2: The twist operator $\sigma_3$. Each loop represents a 'copy' of the CFT wrapping the $S^1$. The twist operator joins these copies into one single copy of the CFT living on a circle of three times the length of the original circle.
• Figure 3: (a) The NS vacuum state in the CFT and (b) its gravity dual, which is global $AdS$. The NS vacuum is the simplest possible state having no twists, no excitations, and no base spin.
• Figure 4: (a) The NS vacuum state in the CFT and (b) the CFT state after spectral flow. The arrows at the center of the circle indicate the 'base spin' of component strings in the Ramond sector. The wavy arrows on top (bottom) of the strands represent fermionic excitations in the left (right) sector.
• Figure 5: The initial and final states for the emission process discussed in Sections \ref{['sec:states-and-op']}, \ref{['sec:CFT-evaluation']}, and \ref{['sec:calc-rate-emission']}. The pictures correspond to $\nu=2$ and $l=1$ emission. The straight arrows pointing up (down) on the loops indicate bosonic excitations in the left (right) sector.