S-duality in $T\bar{T}$-deformed CFT

Abstract

$T\bar{T}$ deformed conformal field theories can be reformulated as worldsheet theories of non-critical strings. We use this correspondence to compute and study the $T\bar{T}$ deformed partition sum of a symmetric product CFT. We find that it takes the form of a partition sum of a second quantized string theory with a worldsheet given by the product of the seed CFT and a gaussian sigma model with the two-torus as target space. We show that deformed symmetric product theory admits a natural UV completion that exhibits a strong weak coupling ${\mathbb{Z}}_2$ duality that interchanges the momentum and winding numbers and maps the $T\bar{T}$-coupling $\lambda$ to its inverse $1/\lambda$. The ${\mathbb{Z}}_2$ duality is part of a full O$(2,2,\mathbb{Z})$-duality group that includes a PSL$(2,\mathbb{Z})$ acting on the complexified $T\bar{T}$ coupling. The duality symmetry eliminates the appearance of complex energies at strong coupling for all seed CFTs with central charge $c\le 6$.

arXiv comment37 pages, v3: JHEP published version, comments, references added, typos corrected

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Cited by in corpus (6)

• Matrix Theory Reloaded: A BPS Road to Holography
• Holographic description of Narain CFTs and their code-based ensembles
• States, symmetries and correlators of $T\bar{T}$ and $J\bar{T}$ symmetric orbifolds
• Asymptotic Symmetries in the TsT/$T\bar{T}$ Correspondence
• String Duals of Two-Dimensional Yang-Mills and Symmetric Product Orbifolds
• Rademacher expansion of modular integrals