Title of Seminar: Infosys Chandrasekharan Random Geometry Colloquium
Title of Talk: `Quantization' and Topological Aspects of the Space of Renormalization Group flows in 2-dim Quantum Field Theory
Speaker: Spenta Wadia, ICTS
Date: July 26, 2021
Time: 16:00:00 Hours
Venue: AG-77
Abstract: In this talk we will discuss a `quantization' of the renormalization group equations by adding a gaussian noise term and converting them into stochastic differential equations. We will discuss the case of two dim. unitary QFTs where a Zamolodchikov $c$-function exists and the `drift term' is a gradient of the c-function. Quantization leads to supersymmetric quantum mechanics which can be studied in the `semi-classical' approximation. In particular one can attempt to characterise the topology of the space of paths in the path integral using Morse theory using the Zamolodchikov $c$-function as a Morse function. Assuming the validity of Morse inequalities in the infinite dimensional case we calculate, as an illustration, the Betti numbers of the space of flows of the $c < 1$ unitary minimal models of 2-dm conformal field theory. This talk is based on work with S. R. Das and G. Mandal: "Stochastic differential equations on 2-dim. theory space and Morse theory", Mod. Phys. Letts A, Vol 4 No.8 (1989).
Title of Talk: `Quantization' and Topological Aspects of the Space of Renormalization Group flows in 2-dim Quantum Field Theory
Speaker: Spenta Wadia, ICTS
Date: July 26, 2021
Time: 16:00:00 Hours
Venue: AG-77
Abstract: In this talk we will discuss a `quantization' of the renormalization group equations by adding a gaussian noise term and converting them into stochastic differential equations. We will discuss the case of two dim. unitary QFTs where a Zamolodchikov $c$-function exists and the `drift term' is a gradient of the c-function. Quantization leads to supersymmetric quantum mechanics which can be studied in the `semi-classical' approximation. In particular one can attempt to characterise the topology of the space of paths in the path integral using Morse theory using the Zamolodchikov $c$-function as a Morse function. Assuming the validity of Morse inequalities in the infinite dimensional case we calculate, as an illustration, the Betti numbers of the space of flows of the $c < 1$ unitary minimal models of 2-dm conformal field theory. This talk is based on work with S. R. Das and G. Mandal: "Stochastic differential equations on 2-dim. theory space and Morse theory", Mod. Phys. Letts A, Vol 4 No.8 (1989).