Symmetries and operators in TT̅ deformed CFTs
- 1Tsinghua University
- 2Harvard University
- 3Peng Huanwu Center for Fundamental Theory
Abstract
A bstract : TT̅ T T ¯ -deformed CFTs are known to possess nonlocal Virasoro×Virasoro symmetries, whose currents depend on integration of the stress tensor. Unfortunately, these symmetries do not act in a tractable manner on the undeformed operators, which are defined by evolving local operators in the undeformed CFT on a constant-time slice using the deformed Hamiltonian. In this paper, we explicitly construct two distinct classes of operators: (i) dressed operators, which are primary with respect to the Virasoro×Virasoro symmetries, and (ii) physical operators, a new type of operator that depends on fundamental fields at specific points and is therefore local at the classical level. While dressed operators preserve the conformal symmetry structure, they are themselves nonlocal in the sense that they depend on integrated quantities. Physical operators, by contrast, depend only on local fields. Moreover, physical operators can be expressed in terms of dressed operators, and this relation can be promoted to a definition of such operators at the quantum level. This enables the use of Virasoro×Virasoro symmetries to systematically compute physical quantities such as correlation functions. We calculate the two-point correlation functions of these operators in momentum space and find that our results align with both string theory predictions and field theory calculations. Additionally, we explore the relationship between physical operators and alternative operator definitions proposed in the literature.
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BibTeX
@article{chen2026symmetries,
title = {{Symmetries and operators in $$ T\overlineT $$ deformed CFTs}},
author = {Liangyu Chen and Zhengyuan Du and Kangning Liu and Wei Song},
journal = {Journal of High Energy Physics},
year = {2026},
month = oct,
doi = {10.1007/jhep10(2026)238},
url = {https://link.springer.com/article/10.1007/JHEP10(2026)238},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Symmetries and operators in TT̅ deformed CFTs
AU - Liangyu Chen
AU - Zhengyuan Du
AU - Kangning Liu
AU - Wei Song
PY - 2026
DA - 2026/10/23
JO - Journal of High Energy Physics
DO - 10.1007/jhep10(2026)238
UR - https://link.springer.com/article/10.1007/JHEP10(2026)238
AB - A bstract : TT̅ T T ¯ -deformed CFTs are known to possess nonlocal Virasoro×Virasoro symmetries, whose currents depend on integration of the stress tensor. Unfortunately, these symmetries do not act in a tractable manner on the undeformed operators, which are defined by evolving local operators in the undeformed CFT on a constant-time slice using the deformed Hamiltonian. In this paper, we explicitly construct two distinct classes of operators: (i) dressed operators, which are primary with respect to the Virasoro×Virasoro symmetries, and (ii) physical operators, a new type of operator that depends on fundamental fields at specific points and is therefore local at the classical level. While dressed operators preserve the conformal symmetry structure, they are themselves nonlocal in the sense that they depend on integrated quantities. Physical operators, by contrast, depend only on local fields. Moreover, physical operators can be expressed in terms of dressed operators, and this relation can be promoted to a definition of such operators at the quantum level. This enables the use of Virasoro×Virasoro symmetries to systematically compute physical quantities such as correlation functions. We calculate the two-point correlation functions of these operators in momentum space and find that our results align with both string theory predictions and field theory calculations. Additionally, we explore the relationship between physical operators and alternative operator definitions proposed in the literature.
SN - 1029-8479
ER -