## Introduction to Conformal Field Theory

Guillermo A. Silva of University of La Plata (Argentina), and visiting professor at FIM-UNIMORE, will give a course on Introduction to Conformal Field Theory. The course will be self-contained and, due to the broadness of the topics, is particularly suitable for all Physics and Math master students and PhD's. Anyone interested is welcome to participate.

**Speaker**: Guillermo A. Silva *(University of La Plata, Argentina)*

**Class hours**: Thursday 11-13, room L1.5, Friday 14-16, room L1.6

**Period**: March 2, May 26

**Duration**: 48 hours (24 lectures)

**Abstract**: This course will provide students with an introduction to conformal symmetry and conformal field theories (CFTs). These theories play a central role in various areas of theoretical physics, ranging from high energy physics and string theory to condensed matter systems, as well as in mathematics. After an extensive discussion of the physical foundations of conformal symmetry and the basics of conformal field theories, emphasis will be given to the study of theories in diverse spacetime dimensions and to the techniques used to solve them.

**Content of the Course**:

- Motivations. Scaling and the renormalization group idea. Momentum integration shells, flows and β-functions. Relevant and irrelevant perturbations. epsilon-expansion. Systems of interest: Ising universality class, vector models, gauge theories. Critical phenomena.
- Conformal group in D-dimensions. Conformal Killing vectors and their algebra. 2d and de Wit algebra. Finite forms. Inversion.

Conformal invariants. Minkowski vs Euclidean signature. Embedding space formalism. - Representations in terms of fields. Primary operators and their scale dimensions. Descendents. Derivative constraints and protected dimensions.
- Conformal invariance in field theory. Symmetries and conserved currents. The energy-momentum tensor. Scalar 2-, 3- and 4-pt correlation functions. Fields with spin s = 1, 2 and inversion.
- Quantization in field theory. Correlators and path integrals. Unitarity and Reflection positivity. States and wave-functionals from path integrals. Symmetries and currents again: Noether theorem and Ward identity.
- Quantization of CFTs. Action of conformal algebra on operators. Euclidean conformal algebra. Radial quantization and operator-state correspondence. Plane and cylinder.
- Non-perturbative methods. Unitarity bounds. OPE and its restrictions. Conformal blocks. Crossing symmetry. Ideas of conformal bootstrap.
- 2d CFTs. Virasoro algebra, conformal anomaly and the central charge. Ward identities, primaries and Tμν in complex coordinates.

[Ultimo aggiornamento: 01/03/2023 15:42:28]