States, symmetries and correlators of $T\bar{T}$ and $J\bar{T}$ symmetric orbifolds

Abstract

We derive various properties of symmetric product orbifolds of $T\bar{T}$ and $J\bar{T}$ - deformed CFTs from a field-theoretical perspective. First, we generalise the known formula for the torus partition function of a symmetric orbifold theory in terms of the one of the seed to non-conformal two-dimensional QFTs; specialising this to seed $T\bar{T}$ and $J\bar{T}$ - deformed CFTs reproduces previous results in the literature. Second, we show that the single-trace $T\bar{T}$ and $J\bar{T}$ deformations preserve the Virasoro and Kac-Moody symmetries of the undeformed symmetric product orbifold CFT, including their fractional counterparts, as well as the KdV charges. Finally, we discuss correlation functions in these theories. By extending a previously-proposed basis of operators for $J\bar{T}$ - deformed CFTs to the single-trace case, we explicitly compute the correlation functions of both untwisted and twisted-sector operators and compare them to an appropriate set of holographic correlators. Our derivations are based mainly on Hilbert space techniques and completely avoid the use of conformal invariance, which is not present in these models.

50 pp, 5 figures

References in corpus (24)

• On space of integrable quantum field theories
• $T\bar{T}$-deformed 2D Quantum Field Theories
• Universal Spectrum of 2d Conformal Field Theory in the Large c Limit
• Nonrelativistic conformal field theories
• Solving the Simplest Theory of Quantum Gravity
• A Solvable Irrelevant Deformation of $Ad{S}_3/CF{T}_2$
• Holography for Schrodinger backgrounds
• A perturbative CFT dual for pure NS-NS AdS${}_3$ strings
• Expectation value of composite field $T\bar{T}$ in two-dimensional quantum field theory
• Correlators of the symmetric product orbifold
• Permutation orbifolds and holography
• On correlation functions in $J\bar{T}$-deformed CFTs
• Deforming Symmetric Product Orbifolds: A tale of moduli and higher spin currents
• Infinite pseudo-conformal symmetries of classical $T\bar{T}$, $J\bar{T}$ and $J{T}_a$ - deformed CFTs
• Solving a family of $T\bar{T}$-like theories
• S-duality in $T\bar{T}$-deformed CFT
• A definition of primary operators in $J\bar{T}$-deformed CFTs
• On the universal behavior of $T\bar{T}$-deformed CFTs: single and double-trace partition functions at large $c$
• Classical and quantum symmetries of $T\bar{T}$-deformed CFTs
• $J\bar{T}$-deformed CFTs as non-local CFTs
• Symmetries versus the spectrum of $J\bar{T}$-deformed CFTs
• Correlation Functions in the TsT/$T\bar{T}$ Correspondence
• $\frac{SL(2,\mathbb{R})\times U(1)}{U(1)}$ CFT, NS5$+$F1 system and single trace $T\bar{T}$
• Comments on the negative specific heat of the $T\bar{T}$ deformed symmetric product CFT

Cited by in corpus (8)

• One-loop partition functions in $T\overline{T}$-deformed AdS${}_3$
• Asymptotic Symmetries in the TsT/$T\bar{T}$ Correspondence
• Systematic approach to correlators in $T\bar{T}$ deformed CFTs
• Correlation Functions in $\text{T}\bar{\text{T}}$-deformed Theories on the Torus
• String Duals of Two-Dimensional Yang-Mills and Symmetric Product Orbifolds
• Root-$T\overline{T}$ deformed CFT partition functions at large central charge
• Lecture notes on strings in AdS${}_3$ from the worldsheet and the AdS${}_3$/CFT${}_2$ duality
• The on-shell action of supergravity & the B-side of TsT and single-trace $T\bar{T}$