# Mathematical Aspects of String Theory 2

Lecture course in the Summer term 2023

This course is a continuation from the Winter term, and it is sought to flank String Theory 2 course, which introduces to superstring theory.

In superstring theory fermions and supersymmetry enter the picture, opening up to a wealth of new possibilities but also requiring a substantial leap in terms of mathematical sophistication. In this course we will introduce the mathematical concepts which lie at the basis of the description of fermions in relativistic field theories and strings.

In particular, in the first part of the course we will describe and classify Clifford algebras and spinor representations in any dimension. In the second part of the course we will move on to geometry, and we will introduce spin manifolds and spin connections, with an eye toward supergravity and superstrings. We will then discuss holonomy groups, parallel and Killing spinors.

If time permits, we will unify bosonic and fermionic geometries introducing the concept of *superspace*.

### Info

**Join the MaMpf & Müsli page of course!**

## Description

##### Instructor

Lecturer: Dr. Simone Noja, Email

##### Time and place

Lectures on Tuesday & Thursday, 16-18, in Mathematikon SR10. **First class on May 2**

##### Prerequisites

A basic understanding of differential geometry, Lie groups and Lie algebras. Attendence to Mathematical Aspects of String Theory 1 might help, but it is not required.

## Bibliography

The notes of the classes are available on MaMf. A *not-at-all* exhaustive list of useful references of the topics covered is given below.

##### Abstract nonsense and category theory

- P. Aluffi,
*Algebra: Chapter 0*, AMS (2009) - S. Mac Lane,
*Categories for the working mathematicians*, Springer (1978) - E. Riehl,
*Category theory in context*, Dover (2016)

##### Clifford algebras, Pin, Spin and all that

- M.F. Atiyah, R. Bott, A. Shapiro,
*Clifford modules*, Topology**3**(1), (1964) 3-28 - H. Blaine Lawson Jr., M.-L. Michelson,
*Spin geometry*, Princeton University Press (1989) - E. Meinrenken,
*Clifford algebras and Lie theory*, Springer (2013)