Exact solutions in 1+1 dimensional supersymmetric sigma models

• Applicant: Dr. Gleb Kotousov
• Subject Area: Nuclear and Elementary Particle Physics, Quantum Mechanics, Relativity, Fields ; Theoretical Condensed Matter Physics
• Term: since 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 566482125

The class of 1+1 dimensional supersymmetric sigma models have many interesting applications in theoretical physics, e.g., to disorder problems. They also turn out to be notoriously difficult to study using conventional techniques. Recently, an exciting possibility for obtaining exact solutions for supersymmetric sigma models has appeared due to developments in quantum integrable systems. It has been discovered that certain integrable critical superspin chains, solvable by means of the Bethe Ansatz, possess phases that are governed by such (conformal) Quantum Field Theories. In this project we study the scaling limit of a two-parameter family of integrable, critical superspin chains. The lattice system exhibits many different types of universal behaviour including one that is expected to be governed by the $SU(2|1)$ WZW model at level $k=1$. We will apply a numerical analysis and the powerful analytic technique of the ODE/IQFT correspondence in order to obtain a field theory description in each of the critical phases. These same methods will enable us to achieve unparalleled insights into the conformal field theory, including the solution of the spectral problem.

• DFG Programme: Research Grants
• International Connection: United Kingdom
• Cooperation Partner: Dr. Sascha Gehrmann