Fluxo do grupo de renormalização dos modelos-'alfa' e as álgebras de Lie contínuas - Roa Aguirre, Alexis [UNESP] (2008)
This work is basically a review of some aspect of the integrability in two dimensions discussed in the Prof. Ioannis Bakas's paper called Renormalization group ﬂows and continual Lie algebras. The main idea is to study the renormalization group ﬂow of two-dimensional metrics in sigma models using the one-loop beta function, and demonstrate that they provide a continual analogue of the Toda ﬁeld equations in conformally ﬂat coordinates in the target space. In this algebraic frame, the logarithm of the world-sheet length scale t is interpreted as Dynkin parameter on the root system of a continual Lie algebra, denoted by G(d/dt;II),witha an ti-symmetric generalized Cartan kernel K(t,t') ='sigmma'(t−t'). Using the zero curvature formalism, we construct a general solution of the renormalization group ﬂow in terms of the free ﬁeld conﬁgurations via B¨acklund transformations. The validity of these general solutions as a power series expansion is veriﬁed in some specials examples including the sausage model, the constant negative curvature metrics and the decay of conical singularities