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

Abstract

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

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

References in corpus (4)

• Leading Logarithms in the Massive O(N) Nonlinear Sigma Model
• Chiral Logarithms Tamed
• Leading Infrared Logarithms from Unitarity, Analyticity and Crossing
• Chiral logarithms to five loops

Cited by in corpus (9)

• Leading logarithms in N-flavour mesonic Chiral Perturbation Theory
• Leading logarithms for the nucleon mass
• Chiral Perturbation Theory Reflections on Effective Theories of the Standard Model
• Exact summation of leading infrared logarithms in 2D effective field theories
• Leading Logarithms of the Two Point Function in Massless O(N) and SU(N) Models to any Order from Analyticity and Unitarity
• Renormalising the Field-Space Geometry
• Quasi-Renormalizable Quantum Field Theories
• Leading chiral logarithms for the nucleon mass
• Exact summation of leading logs around $T\bar{T}$ deformation of $O(N+1)$-symmetric 2D QFTs