From symmetric product CFTs to AdS3

We examine the question how string theory achieves a sum over bulk geometries with fixed asymptotic boundary conditions. We discuss this problem with the help of the tensionless string on $$ {\mathrm{\mathcal{M}}}_3\times {\mathrm{S}}^3\times {\mathbbm{T}}^4 $$ ℳ 3 × S 3 × T 4 (with one unit of NS-NS flux) that was recently understood to be dual to the symmetric orbifold SymN ($$ {\mathbbm{T}}^4 $$ T 4 ). We strengthen the analysis of [1] and show that the perturbative string partition function around a fixed bulk background already includes a sum over semi-classical geometries and large stringy corrections can be interpreted as various semi-classical geometries. We argue in particular that the string partition function on a Euclidean wormhole geometry factorizes completely into factors associated to the two boundaries of spacetime. Central to this is the remarkable property of the moduli space integral of string theory to localize on covering spaces of the conformal boundary of ℳ3. We also emphasize the fact that string perturbation theory computes the grand canonical partition function of the family of theories ⊕N SymN ($$ {\mathbbm{T}}^4 $$ T 4 ). The boundary partition function is naturally expressed as a sum over winding worldsheets, each of which we interpret as a ‘stringy geometry’. We argue that the semi-classical bulk geometry can be understood as a condensate of such stringy geometries. We also briefly discuss the effect of ensemble averaging over the Narain moduli space of $$ {\mathbbm{T}}^4 $$ T 4 and of deforming away from the orbifold by the marginal deformation.

Section: Jhep05(2021)233mentioning

confidence: 99%

Summing over geometries in string theory

Eberhardt

2021

“…1 Finally, pure NS-NS AdS 3 backgrounds are conjectured to be related to symmetric product orbifold CFTs [15]. This connection is sharpest for the superstring on AdS 3 × S 3 × T 4 with one unit of NS-NS flux where the dual CFT is conjectured to be the symmetric orbifold of the T 4 sigma-model [16][17][18][19][20][21][22][23]. In this instance, string perturbation theory truncates and there do not seem to be any non-perturbative phenomena.…”

Section: Introductionmentioning

confidence: 96%

String correlators on AdS3: three-point functions

Dei

Eberhardt

2021

We revisit the computation of string worldsheet correlators on Euclidean AdS3 with pure NS-NS background. We compute correlation functions with insertions of spectrally flowed operators. We explicitly solve all the known constraints of the model and for the first time conjecture a closed formula for three-point functions with arbitrary amount of spectral flow. We explain the relation of our results with previous computations in the literature and derive the fusion rules of the model. This paper is the first in a series with several installments.

“…The explicit construction of these functions remains an active area of research [34][35][36][37][38][39][40][41][42][43][44]. In fact, the study of the (T 4 ) N /S N orbifold SCFT has been associated with the development of an explicit realization of AdS 3 /CFT 2 by mapping the D1-D5 system to the F1-NS5 system by S-duality, and working on the AdS 3 × S 3 × T 4 background with only (one unit of) NS fluxes [44][45][46][47][48][49][50][51].…”

Section: Introductionmentioning

confidence: 99%

On the dynamics of protected ramond ground states in the D1-D5 CFT

Lima

Sotkov

Stanishkov

2021

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 ($$ {\mathbbm{T}}^4 $$ 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 $$ \mathcal{N} $$ N = (4, 4) superconformal algebra with central charge c = 6N.