Renormalization group flows and continual Lie algebras

Renormalization group flows and continual Lie algebras

We study the renormalization group flows of two-dimensional metrics in sigma models using the one-loop beta functions, and demonstrate that they provide a continual analogue of the Toda field equations in conformally flat coordinates. In this algebraic setting, the logarithm of the world-sheet length scale, t, is interpreted as Dynkin parameter on the root system of a novel continual Lie algebr...

Optimized renormalization group flows

We study the optimization of exact renormalization group ~ERG! flows. We explain why the convergence of approximate solutions towards the physical theory is optimized by appropriate choices of the regularization. We consider specific optimized regulators for bosonic and fermionic fields and compare the optimized ERG flows with generic ones. This is done up to second order in the derivative expa...

Aspects of Renormalization Group Flows

Renormalization group equations and geometric flows

The quantum field theory of two-dimensional sigma models with bulk and boundary couplings provides a natural framework to realize and unite different species of geometric flows that are of current interest in mathematics. In particular, the bulk renormalization group equation gives rise to the Ricci flow of target space metrics, to lowest order in perturbation theory, whereas the boundary renor...

Derivative expansion and renormalization group flows

We study the convergence of the derivative expansion for flow equations. The convergence strongly depends on the choice for the infrared regularisation. Based on the structure of the flow, we explain why optimised regulators lead to better physical predictions. This is applied to O(N)-symmetric real scalar field theories in 3d, where critical exponents are computed for all N . In comparison to ...