Expectation value of $\mathrm{T}\overline{\mathrm{T}}$ operator in curved spacetimes

Abstract

We study the expectation value of the $\mathrm{T}\overline{\mathrm{T}}$ operator in spacetimes with constant curvature. We define an diffeomorphism invariant biscalar whose coinciding limit gives the expectation value of the $\mathrm{T}\overline{\mathrm{T}}$ operator. We show that this biscalar is a constant in flat spacetime, which reproduces Zamolodchikov's result in 2004. For spacetimes with non-zero curvature, we show that this is no longer true and the expectation value of the $\mathrm{T}\overline{\mathrm{T}}$ operator depends on both the one-point and two-point functions of the stress-energy tensor.

Minor modifications, journal version

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Cited by in corpus (25)

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• The correlation function of (1,1) and (2,2) supersymmetric theories with $T\bar{T}$ deformation
• Gravitational path integral from the $T^2$ deformation
• Geometrizing $T\bar{T}$
• 3D Gravity in a Box
• $T\bar{T}$ in JT Gravity and BF Gauge Theory
• Field Theory of Interacting Boundary Gravitons
• Cutoff $\mathrm{Ad}{\mathrm{S}}_3$ versus $\mathrm{T}\bar{\mathrm{T}}$ $\mathrm{CF}{\mathrm{T}}_2$ in the large central charge sector: correlators of energy-momentum tensor
• Stress Tensor Flows, Birefringence in Non-Linear Electrodynamics, and Supersymmetry
• Glue-on AdS holography for $T\bar{T}$-deformed CFTs
• $T\bar{T}$-flow effects on torus partition functions
• Quantum corrections to finite radius holography and holographic entanglement entropy
• Building Tensor Networks for Holographic States
• $T\overline{T}$ deformation in SCFTs and integrable supersymmetric theories
• $T\overline{T}$ Deformations of Supersymmetric Quantum Mechanics
• A Path Integral Realization of Joint $J\bar{T}$, $T\bar{J}$ and $T\bar{T}$ Flows
• End of the World Brane meets $T\bar{T}$
• $T\overline{T}$-deformation of $q$-Yang-Mills theory
• Irrelevant Deformations of Chiral Bosons
• Holographic $T\bar{T}$ deformation of the entanglement entropy in (A)dS${}_3$/CFT${}_2$
• Demystifying integrable QFTs in AdS: No-go theorems for higher-spin charges
• Holographic boundary conformal field theory with $T\bar{T}$ deformation