## “The content [covered in Differential Geometry and Symmetry] was very interesting, I did not know this field existed, or that it could be done, but now I have seen the technologies that people use to understand non-euclidean geometry from a function-analysis perspective, and I like that.”

Jarvis Caroll, University of Tasmania

# Introduction to String Theory

#### Lecturers

Dr. Johanna Knapp, The University of Melbourne

#### Synopsis

String theory is a physical theory that unifies the known fundamental forces of nature at the quantum level. Point particles are replaced by fundamental strings. This concept has far reaching consequences, including extra dimensions, “stringy” dualities, and intricate mathematical structures. This course will cover the basic concepts and is intended to provide the foundations for further (self-)study and research projects in string theory. The course aims to be mostly self-contained and should be suitable also for students who do not necessarily have a background in physics.

#### Course Overview

• The classical bosonic string: Polyakov action, symmetries, equations of motion and their solution
• The quantised bosonic string: quantisation, spectrum and unification of forces, conformal anomaly and extra dimensions, compactification on a circle and T-duality
• Introduction to conformal field theory: basic concepts and application to string theory

#### Prerequisites

• String theory touches many areas of mathematics and physics, so it does not make much sense to select specific topics as prerequisites. So there will be *no prerequisites*. However, if you have basic knowledge about any of the following topics, some of the concepts may be easier to understand for you: complex analysis (residue theorem), Fourier series, the wave equation, the harmonic oscillator, basic classical and/or quantum mechanics. No knowledge of advanced concepts of theoretical physics, such as general relativity or quantum field theory, is required.

#### Assessment

• Regular quizzes, 10% total
• Two assignments, 15% each
• Written exam, 60%

Lecture notes will be provided during the course.

• The course is mostly based on the book “Basic Concepts of String Theory” by Blumenhagen, Lust, Theisen. We will cover chapters 2-5 and, if time permits, some aspects of later chapters.