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Asymptotic Symmetries in the TsT/T\bar{T} Correspondence
by Zhengyuan Du; Wen-Xin Lai; Kangning Liu; Wei Song
Submission summary
| Authors (as registered SciPost users): | Zhengyuan Du · Wen-Xin Lai · Kangning Liu |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202409_00009v2 (pdf) |
| Date submitted: | 2024-12-03 08:51 |
| Submitted by: | Liu, Kangning |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
Starting from holography for IIB string theory on AdS$_3\times \mathcal N$ with NS-NS flux, the TsT/$T\bar T$ correspondence is a conjecture that a TsT transformation on the string theory side is holographically dual to the single-trace version of the $T\bar T$ deformation on the field theory side. More precisely, the long string sector of string theory on the TsT-transformed background corresponds to the symmetric product theory whose seed theory is the $T\bar T$-deformed CFT$_2$. In this paper, we study the asymptotic symmetry of the string theory in the bulk. We find a state-dependent, non-local field redefinition under which the worldsheet equations of motion, stress tensor, as well as the symplectic form of string theory after the TsT transformation are mapped to those before the TsT transformation. The asymptotic symmetry in the auxiliary AdS basis is generated by two commuting Virasoro generators, while in the TsT transformed basis is non-linear and non-local. Our result from string theory analysis is compatible with that of the $T\bar T$ deformed CFT$_2$.
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List of changes
1. We added a new subsection 5.1 and some comments below (101).
2. We added some comments above section 5.4.
3. We added some comments below equation (54) and (64).
4. We added “in the fixed w sector” on page 15 above equation (64).
5. We added a sentence below equation (94).
6. Typos in equation (9), (24), (26), (29), (50), (66), (96) are corrected. A sentence in the first lines on page 18 is rewritten.
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