Correlation functions of symmetric orbifold from AdS 3 string theory
- PDF / 564,853 Bytes
- 32 Pages / 595.276 x 841.89 pts (A4) Page_size
- 22 Downloads / 226 Views
Springer
Received: June 1, Revised: August 12, Accepted: August 19, Published: September 23,
2020 2020 2020 2020
Yasuaki Hikida and Tianshu Liu Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa Oiwakecho, Sakyo-ku, Kyoto 606-8502, Japan
E-mail: [email protected], [email protected] Abstract: 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. Keywords: AdS-CFT Correspondence, Conformal Field Models in String Theory, Conformal Field Theory ArXiv ePrint: 2005.12511
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP09(2020)157
JHEP09(2020)157
Correlation functions of symmetric orbifold from AdS3 string theory
Contents 1 Introduction
1
2 Correlation functions in symmetric orbifold
4 8 8 9 12 16
4 Higher genus extension 4.1 Higher genus Riemann surface 4.2 Correlation functions in symmetric orbifold 4.3 Correlation functions in sl(2) WZNW model
19 19 21 22
5 Conclusion and open problems
25
A Correlation functions of ghost system
27
1
Introduction
It is widely believed that there appears an enhanced higher spin symmetry at the tensionless limit of superstring theory and the symmetry enables us to treat its stringy effects [1]. At the same time, the tensionless limit of superstrings can be argued to be dual to a weakly coupled conformal field theory (CFT). Therefore, we can make a quantitative check of AdS/CFT correspondence including the stringy effects by making use of the tensionless limit. Recently, it was claimed that a tensionless limit of superstrings on AdS 3 × S 3 × T 4 with NSNS-flux is exactly dual to the symmetric orbifold T 4 /SN . 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 [5–8] for previous works. We first obtain the correlation functions of symmetric orbifold by following the method developed in [9, 10]. These correlation functions are then compared with those of AdS3 string theory computed by applying findings of the previou
Data Loading...
