Speaker
Dr
Alessandro Codello
Description
After reviewing the Functional reformulation of the standard Perturbative RG (FPRG), I'll describe the classification of universality classes in arbitrary dimension within the epsilon-expansion and the relative determination of CFT data.
In the single component case, universality classes are represented by renormalizable scalar QFTs with self-interacting potentials of highest monomial φ^m below their upper critical dimensions dc = 2m/(m -2). For even integers, m ≥ 4 these theories coincide with the Landau-Ginzburg description of multi-critical phenomena and interpolate with the unitary minimal models in d = 2, while for odd m the theories are non-unitary and start at m = 3 with the Lee-Yang universality class.
An important outcome of this analysis is the realization of the existence of a new non-trivial family of d = 3 universality classes with upper critical dimension dc = 10/3.
Subsequently, I will show how the FPRG formalism allows a straightforward generalization to the multicomponent case, with almost no need for additional computations. The classification of multicomponent universality classes if far from complete and I will discuss the present state of knowledge with few examples, including Potts and O(N) models.
I will conclude with a review and outlook of the application of the epsilon-expansion to Quantum Gravity.
