Dynamics of chiral primaries in $AdS_3 \times S^3 \times T^4$

TL;DR

The paper builds a bridge between the gravity dynamics of 1/2 BPS configurations in AdS$_3\times$S$^3$ and the $(S_N)$-orbifold collective field theory for chiral primaries in the D1-D5 system. It identifies two gravity-side chiral primaries, derives their linearized actions from the six-dimensional SUGRA reduced on AdS$_3\times$S$^3$, and computes the full nonlinear symplectic structure using the covariant CWZ formalism. A key result is the explicit transformation that maps the curve fluctuations $F_i(u)$ to collective-field variables, producing a cubic vertex consistent with the $S_N$ collective theory, thereby linking a 1D fermionic droplet picture to AdS$_3$/CFT$_2$ dynamics. The findings reinforce the integrable structure of the BPS sector and lay groundwork for extending to more general 3-charge configurations and the microstate (supertube/black hole) program. The work thus provides a concrete gravity–CFT dictionary at the level of Hamiltonians and symplectic forms for chiral primaries.

Abstract

We study in more detail the dynamics of chiral primaries of the D1/D5 system. From the CFT given by the $S_{n}$ orbifold a study of correlators resulted in an interacting (collective) theory of chiral operators. In $AdS_{3}\times S^{3}$ SUGRA we concentrate on general 1/2 BPS configurations described in terms of a fundamental string .We first establish a correspondence with the linerized field fluctuations and then present the nonlinear analysis. We evaluate in detail the symplectic form of the general degrees of freedom in Sugra and confirm the appearance of chiral bosons. We then discuss the apearance of interactions and the cubic vertex,in correspondence with the $S_{N}$ collective field theory representation.