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 ( {mathbbm{T}}^4 )N/SN 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 SN 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.
Highlights
Asymptotically flat black ring at spatial infinity, with six large dimensions, whose geometry becomes AdS3 × S3 × T4 in the near-horizon scaling limit,2 and whose Bekenstein-Hawking entropy was derived microscopically by Strominger and Vafa [3]
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 (T4)N /SN by a marginal interaction operator
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 N = (4, 4) superconformal algebra with central charge c = 6N
Summary
The Ramond ground states of the orbifold with c = 6N are compositions of single-cycle fields with disjoint twists defining a conjugacy class of SN , i(R(ζni i))qi , i=1 niqi = N ,. Since each component of the product is made from different copies (i.e. the cycles (ni) are disjoint), when applying the stress-tensor or the SU(2) currents, we find that the dimension and the charges of the composite operator are the sums of the respective quantum numbers of the component strings, hR = i qini = N = hR. I.e. we permute all cycles with the same h ∈ SN , ensuring that only disjoint cycles enter the products of twists This is similar to defining a “normal ordering”, see [41, 68], which we indicate by writing the composite operator inside square brackets.
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