S-duality in T T ¯ $$ T\overline{T} $$ -deformed CFT

Abstract

Abstract T T ¯ $$ T\overline{T} $$ deformed conformal field theories can be reformulated as worldsheet theories of non-critical strings. We use this correspondence to compute and study the T T ¯ $$ T\overline{T} $$ 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 ℤ2 duality that interchanges the momentum and winding numbers and maps the T T ¯ $$ T\overline{T} $$ -coupling λ to its inverse 1/λ. The ℤ2 duality is part of a full O(2, 2, ℤ)-duality group that includes a PSL(2, ℤ) acting on the complexified T T ¯ $$ T\overline{T} $$ coupling. The duality symmetry eliminates the appearance of complex energies at strong coupling for all seed CFTs with central charge c ≤ 6.

Keywords

• Bosonic Strings
• Field Theories in Lower Dimensions
• Scale and Conformal Symmetries
• String Duality