Correlators of the symmetric product orbifold

Self Cite

271

We employ the free field realisation of the $$ \mathfrak{psu}{\left(1,1\left|2\right.\right)}_1 $$ psu 1 1 2 1 world-sheet theory to constrain the correlators of string theory on AdS3× S3× 𝕋4 with unit NS-NS flux. In particular, we directly obtain the unusual delta function localisation of these correlators onto branched covers of the boundary S2 by the (genus zero) world-sheet — this is the key property which makes the equivalence to the dual symmetric orbifold manifest. In our approach, this feature follows from a remarkable ‘incidence relation’ obeyed by the correlators, which is reminiscent of a twistorial string description. We also illustrate our results with explicit computations in various special cases.

Section: Constraining the Correlation Functionssupporting

confidence: 75%

“…The action S L [φ cl ] is to be evaluated in a suitably regularised way [4]. Together with the results of [33], this then suggests that the full correlator (combining both chiral and anti-chiral degrees of freedom) is of the form…”

Section: Constraining the Correlation Functionsmentioning

confidence: 99%

Free field world-sheet correlators for AdS3

Dei

Gaberdiel

Gopakumar

et al. 2021

Self Cite

271

“…As a support, the match of spectrum was already shown in [2,3], see also [4]. In this paper, we examine the correspondence of correlation functions in the duality described above, see [5][6][7][8] for previous works. We first obtain the correlation functions of symmetric orbifold by following the method developed in [9,10].…”

Section: Introductionsupporting

confidence: 53%

“…For this, we set w = −1 for the vertex operator at z = y as in (3.48). 7 Since the vertex operators in (3.48) do not involve β explicitly, we can integrate β out, which yields∂γ = 0. This means that γ should be replaced by a meromorphic function of z.…”

Section: Jhep09(2020)157mentioning

confidence: 99%

Correlation functions of symmetric orbifold from AdS3 string theory

Hikida

Liu

2020

The paper examines correspondence among correlation functions of symmetric orbifold and string theory on AdS3 described by sl(2) Wess-Zumino-Novikov-Witten (WZNW) model. We start by writing down n-point function of twist operators in the symmetric orbifold in terms of the data of effective Riemann surface. It is then shown that the correlation function can be reproduced from the sl(2) WZNW model. The computation is based on the claim that string worldsheet is given by the same Riemann surface and the reduction method from sl(2) WZNW model to Liouville field theory. We first consider the genus zero surface and then generalize the analysis to the case of generic genus. The radius of AdS3 is related to the level k of the WZNW model. For k = 3, our result should be an important ingredient for deriving AdS3/CFT2 correspondence with tensionless superstrings to all orders in string perturbation theory. For generic k, relations involving specific forms of correlation functions for strings on AdS3× X were obtained.

“…Furthermore, this k > 1 generalisation also seems to apply to the bosonic set-up for which there is a relation between string theory on AdS 3 ×X at the WZW point [7], and the symmetric orbifold of Liouville theory times X [6]. Some aspects of this bosonic correspondence were tested further in [8,9]. In particular,…”

Section: Introductionmentioning

confidence: 92%

Stress-energy tensor correlators from the world-sheet

Bertle

Dei

Gaberdiel

2021

Self Cite

The large N limit of symmetric orbifold theories was recently argued to have an AdS/CFT dual world-sheet description in terms of an sl(2, ℝ) WZW model. In previous work the world-sheet state corresponding to the symmetric orbifold stress-energy tensor was identified. We calculate certain 2- and 3-point functions of the corresponding vertex operator on the world-sheet, and demonstrate that these amplitudes reproduce exactly what one expects from the dual symmetric orbifold perspective.