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

TL;DR

This paper investigates the structure of nonlocal charges arising from marginal deformations of 2D conformal field theories, with applications to holographic and integrable deformations, proposing a new algebraic approach for their construction.

Contribution

It introduces a brute force method to compute nonlocal charges for general Lie algebras in deformed 2D CFTs, extending beyond previous free-field techniques.

Findings

Nonlocal charges can be associated with a new Lie algebra-valued field.

Constraints on the algebra of nonlocal charges are derived.

Applications to Yang-Baxter and holographic deformations are discussed.

Abstract

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.