On the Dynamics of Protected Ramond Ground States in the D1-D5 CFT

TL;DR

This paper studies how protected Ramond ground states in the D1-D5 CFT behave under deformations, showing they remain protected and analyzing their four-point functions and operator product expansions.

Contribution

It provides explicit calculations of four-point functions and structure constants, demonstrating the protection of Ramond ground states against deformations in the D1-D5 CFT.

Findings

Ramond ground states remain protected under deformations

Explicit four-point functions and structure constants computed

Protection confirmed through vanishing integrals of four-point functions

Abstract

We examine the behavior of the Ramond ground states in the D1-D5 CFT after a deformation of the free-orbifold sigma model on target space $({\mathbb T}^4)^N / S_N$ by a marginal interaction operator. These states are compositions of Ramond ground states of the twisted and untwisted sectors. They are characterized by a conjugacy class of $S_N$ and by the set of their "spins", including both R-charge and "internal" SU(2) charge. We compute the four-point functions of an arbitrary Ramond ground state with its conjugate and two interaction operators, for genus-zero covering surfaces representing the leading orders in the large-$N$ expansion. We examine short distance limits of these four-point functions, shedding light on the dynamics of the interacting theory. We find the OPEs and a collection of structure constants of the ground states with the interaction operators and a set of resulting non-BPS twisted operators. We also calculate the integrals of the four-point functions over the positions of the interaction operators and show that they vanish. This provides an explicit demonstration that the Ramond ground states remain protected against deformations away of the free orbifold point, as expected from algebraic considerations using the spectral flow of the ${\mathcal N} = (4,4)$ superconformal algebra with central charge $c = 6N$.