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We deform two-dimensional quantum field theories by antisymmetriccombinations of their conserved currents that generalize Smirnov andZamolodchikov's $T\bar{T}$ deformation. We obtain that energy levels on acircle obey a transport equation analogous to the Burgers equation found in the$T\bar{T}$ case. This equation relates charges at any value of the deformationparameter to charges in the presence of a (generalized) Wilson line. Wedetermine the initial data and solve the transport equations for antisymmetriccombinations of flavor symmetry currents and the stress tensor starting fromconformal field theories. Among the theories we solve is a conformal fieldtheory deformed by $J\bar{T}$ and $T\bar{T}$ simultaneously. We check ouranswer against results from AdS/CFT.

Solving a family of $T\bar{T}$-like theories