After reviewing the Functional reformulation of the standard Perturbative RG (FPRG), the speaker will first describe the classification of universality classes in arbitrary dimension within the Epsilon-expansion and the relative determination of Conformal Field Theory (CFT) data.
In the single component case, universality classes are represented by renormalizable scalar Quantum Field Theories (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.
The speaker will also 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 is far from complete and he will discuss the present state of knowledge with few examples, including Potts and O(N) models.
The speaker will conclude with a review and an outlook of the application of the Epsilon-expansion to Quantum Gravity.
