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A bstract $$ T\overline{T} $$ T T ¯ deformed conformal field theories can be reformulated as worldsheet theories of noncritical strings. We use this correspondence to compute and study the $$ T\overline{T} $$ T 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 twotorus 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 $$ T\overline{T} $$ T T ¯ coupling λ to its inverse 1/ λ . 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 $$ T\overline{T} $$ T T ¯ coupling. The duality symmetry eliminates the appearance of complex energies at strong coupling for all seed CFTs with central charge c ≤ 6.Free, publiclyaccessible full text available May 1, 2024

A bstract A twodimensional CFT dual to a semiclassical theory of gravity in three dimensions must have a large central charge c and a sparse low energy spectrum. This constrains the OPE coefficients and density of states of the CFT via the conformal bootstrap. We define an ensemble of CFT data by averaging over OPE coefficients subject to these bootstrap constraints, and show that calculations in this ensemble reproduce semiclassical 3D gravity. We analyze a wide variety of gravitational solutions, both in pure Einstein gravity and gravity coupled to massive point particles, including Euclidean wormholes with multiple boundaries and higher topology spacetimes with a single boundary. In all cases we find that the onshell action of gravity agrees with the ensembleaveraged CFT at large c . The oneloop corrections also match in the cases where they have been computed. We also show that the bulk effective theory has random couplings induced by wormholes, providing a controlled, semiclassical realization of the mechanism of Coleman, Giddings, and Strominger.Free, publiclyaccessible full text available December 1, 2023

A bstract We obtain an asymptotic formula for the average value of the operator product expansion coefficients of any unitary, compact two dimensional CFT with c > 1. This formula is valid when one or more of the operators has large dimension or — in the presence of a twist gap — has large spin. Our formula is universal in the sense that it depends only on the central charge and not on any other details of the theory. This result unifies all previous asymptotic formulas for CFT2 structure constants, including those derived from crossing symmetry of four point functions, modular covariance of torus correlation functions, and higher genus modular invariance. We determine this formula at finite central charge by deriving crossing kernels for higher genus crossing equations, which give analytic control over the structure constants even in the absence of exact knowledge of the conformal blocks. The higher genus modular kernels are obtained by sewing together the elementary kernels for fourpoint crossing and modular transforms of torus onepoint functions. Our asymptotic formula is related to the DOZZ formula for the structure constants of Liouville theory, and makes precise the sense in which Liouville theory governs the universal dynamics ofmore »