S-duality in T(T)over-bar-deformed CFT

T (T) over bar 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) over bar 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 Z(2) duality that interchanges the momentum and winding numbers and maps the T (T) over bar -coupling lambda to its inverse 1/lambda. The Z(2) duality is part of a full O(2, 2, Z)-duality group that includes a PSL(2, Z) acting on the complexified T (T) over bar coupling. The duality symmetry eliminates the appearance of complex energies at strong coupling for all seed CFTs with central charge c <= 6.

Automated summary

T(T) over bar 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) over bar 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 Z(2) duality that interchanges the momentum and winding numbers and maps the T(T) over bar-coupling lambda to its inverse 1/lambda. The Z(2) duality is part of a full O(2, 2, Z)-duality group that includes a PSL(2, Z) acting on the complexified T(T) over bar coupling. The duality symmetry eliminates the appearance of complex energies at strong coupling for all seed CFTs with central charge c <= 6.