Functional Renormalization Group (Lecture III)

Who: Alessandro Codello (CP3-Origins)
When: Thursday, January 21, 2016 at 14:30
Where: The CP³ meeting room

The mini course on the Functional Renormalization Group consists of 4 lectures of 1-2 hours.
All the lectures will be in the CP3 meeting room at 14:30 and will be recorded.

The topics of the lectures are:
1) Renormalization group and exact flow equations
We review the conceptual framework underlying the renormalization group (RG) approach and introduce its modern implementation via an exact RG flow equation for the scale dependent effective action.

2) Approximations: vertex, derivative and loop expansions
The exact RG flow equation is generally to difficult to be solved exactly: approximations schemes are key to its practical use. We introduce the three basic approximations commonly used and discuss their merits, in this way starting to get used to the formalism.

3) Scalar theories and their (functional) fixed points in arbitrary dimensions
We study scalar theories in arbitrary dimensions via the local potential approximation, assuming no prior knowledge of the theory. In the process we will describe the Wilson-Fisher fixed point in d = 3 and “discover” the CFT minimal models in d = 2. We also show how compute in a non-perturbative way universal quantities like critical exponents and discuss how to control the error on these estimations.


Slides from the talk


4) Perturbative vs non-perturbative beta functions
We discuss the relation between the usual perturbative RG approach and the non-perturbative approach based on the exact RG flow equation discussed in the previous lectures. The case of the computation of the two loop beta function for a d = 4 scalar theory is particularly illuminating and we will use it as an example.