Nonlocal charges from marginal deformations of 2D CFTs: Holographic TT¯ & TJ¯, and Yang-Baxter deformations

In this paper we study generic features of nonlocal charges obtained from marginal deformations of Wess-Zumino-Novikov-Witten models. Using free-field 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 TT ̄and TJ ̄ deformations are also discussed.