Leading infrared logarithms for sigma-model with fields on arbitrary Riemann manifold

Details Leading infrared logarithms for sigma-model with fields on arbitrary Riemann manifold Leading infrared logarithms for sigma-model with fields on arbitrary Riemann manifold

2010-12-19

arxiv.org/abs/1012.4205v1

Physics

High Energy Physics

High Energy Physics - Theory

Talk given by MVP at the conference devoted to memory of A.N. Vasiliev

Scientific paper

We derive non-linear recursion equation for the leading infrared logarithms (LL) in four dimensional sigma-model with fields on an arbitrary Riemann manifold. The derived equation allows one to compute leading infrared logarithms to essentially unlimited loop order in terms of geometric characteristics of the Riemann manifold. We reduce the solution of the SU(oo) principal chiral field in arbitrary number of dimensions in the LL approximation to the solution of very simple recursive equation. This result paves a way to the solution of the model in arbitrary number of dimensions at N-->oo

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