Strings, Symmetric Products, $T\bar{T}$ deformations and Hecke Operators

Abstract

We derive a formula for the torus partition sum of the symmetric product of $T\bar{T}$ deformed CFT's, using previous work on long strings in (deformed) $Ad{S}_3$, and universality. The result is given by an integral transform of the partition function for the block of the symmetric product, summed over its Hecke transforms, and is manifestly modular invariant. The spectrum is interpretable as a gas of multiply wound long strings with a particular orientation.

10 pages. v2: reference added

References in corpus (1)

• On space of integrable quantum field theories

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• Supersymmetric black holes and $T\bar{T}$ deformation
• Solvable time-like cosets and holography beyond $AdS$
• Characters of irrelevant deformations
• Strings in Irrelevant Deformations of $Ad{S}_3/CF{T}_2$
• Comments on the negative specific heat of the $T\bar{T}$ deformed symmetric product CFT
• The on-shell action of supergravity & the B-side of TsT and single-trace $T\bar{T}$