SPACE, TIME AND FUNDAMENTAL INTERACTIONS

INTEGRABILITY IN STRING THEORY AND M-THEORY

Gubarev K.A.

In this paper we will demonstrate two facts indicating the existence of an analogue of integrability for threedimensional systems, in particular the M2-brane in M-theory. To do this, we will consider the natural formulation of three-dimensional systems in terms of the Nambu bracket and its connection with the generalized Yang-Baxter equation. We will discuss Yang–Baxter deformations that preserve the integrability of sigma models and in which the classical Yang–Baxter equation naturally arises. We will then present a generalization of the Yang–Baxter deformations to the M-theory case, in which a generalized Yang–Baxter equation arises in a similar way.