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.
Highlights
We address it in the present section, and, in particular, we discuss some ideas about a complete development of new techniques to build and unveil the algebra of nonlocal charges in more general WZNW models
Given that the construction so far has been intrinsically quantum, we need to take it as an advantage to make Ansätze for the operator product expansions (OPEs), and try to see what the physical constraints have to say about the coefficients
With this deformation we can apply the techniques we developed in previous sections regarding the existence and algebraic relations of the nonlocal charges
Summary
Integrable deformations of conformal theories form a powerful method to probe physics near a fixed point theory. It is mandatory to develop methods to study the resulting symmetries when we leave the fixed point theory, and it means that we need to consider relevant deformations of CFTs. The resulting massive theories are quite generally harder than the undeformed models, but one might hope for some progress towards their understanding if we assume integrable deformations of the CFTs. One remarkable example of an exactly marginal perturbation in four dimensions is given by the Leigh-Strassler deformations of N 1⁄4 4 Super Yang-Mills [2], which give conformal theories with N 1⁄4 1 supersymmetry. Associating these new integrable backgrounds to their elusive holographic dual, one can learn a great deal about the surprising mathematical and physical aspects of a vast collection of quantum field theories; see [11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42] for a nonexhaustive list of references
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