Nonlocal charges from marginal deformations of 2D CFTs: Holographic $T \bar T$ and $T \bar J$ and Yang-Baxter deformations.

In this paper we study generic features of nonlocal charges obtained from marginal deformations of WZNW models. Using free fields representations of CFTs based on simply-laced Lie algebras one can use simple arguments to build the nonlocal charges; but for more general Lie algebras these methods are not strong enough to be generally used. We propose a brute force calculation where the nonlocality is associated to a new Lie algebra valued field, and from this prescription we impose several constraints on the algebra of nonlocal charges. Possible applications for Yang-Baxter and holographic $T\bar{T}$ and $T\bar{J}$ deformations are also discussed.