Integrable structure of the string theory

Abstract

The main focus of this proposal is to further examine the integrable structure of the String Theory, beyond the classical level, by means of the quantum inverse scattering method developed by Faddeev, Sklyanin and others. However, the well-known quantization procedure is not applicable due to difficulties such as ambiguities present in the theory at the classical level and various gauge symmetries of the string action that require a very careful treatment. The proposed project aims to address these issues systematically. The realization of this specific program will be an important step towards the quantization of String Theory on AdS backgrounds, understanding its integrable structure on both classical and quantum levels and elucidating its relation to the supersymmetric and non-supersymmetric Yang-Mills theories. (AU)