Information theory and renormalization group flows

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...

Renormalization-group flows and charge transmutation in string theory

We analyze the behaviour of heterotic squashed-Wess–Zumino–Witten backgrounds under renormalization-group flow. The flows we consider are driven by perturbation creating extra gauge fluxes. We show how the conformal point acts as an attractor from both the target-space and world-sheet points of view. We also address the question of instabilities created by the presence of closed time-like curve...

Renormalization Group Techniques to Classical Information Theory

We apply Renormalization Group (RG) techniques to Classical Information Theory, in the limit of large codeword size n. In particular, we apply RG techniques to (1) noiseless coding (i.e., a coding used for compression) and (2) noisy coding (i.e., a coding used for channel transmission). Shannon’s “first” and “second” theorems refer to (1) and (2), respectively. Our RG technique uses composition...

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...