This course is an introduction to branes in string theory and their world volume dynamics. Instead of looking at the theory from the point of view of the world-sheet observer, we will approach the problem from the point of view of an observer which lives on a brane. Instead of writing down conformal field theory on the world-sheet and studying the properties of these theories, we will look at various branes in string theory and ask how the physics on their world-volume looks like.

Syllabus

Prerequisite

Relativistic Quantum Field Theory I (8.323)

Overview

This course is an introduction to branes in string theory and their world-volume dynamics. The theme of the course will be different from the traditional approach of teaching string theory. Instead of looking at the theory from the point of view of the world-sheet observer, we will approach the problem from the point of view of an observer which lives on a brane. Instead of writing down conformal field theory on the world-sheet and studying the properties of these theories, we will look at various branes in string theory and ask how the physics on their world-volume looks like. This will give a totally different approach than the usual CFT approach on the world-sheet and will give new intuition and new insights on how we should think and understand string theory in various dimensions and supersymmetries. This approach is relatively new. It is a result of the change in thinking the world of string theory had gone through in the past 10 years. During this period researchers in the field begun to understand the importance of branes in string theory and the crucial role they play in various phenomena. The realization that branes are crucial in string theory then led to an opening of a whole new world of research that has to do with the dynamics of supersymmetric gauge theories and quantum field theories on the world-volume of branes in various dimensions and supersymmetries.

Objectives

By the end of this course, we should be able to take an arbitrary configuration of branes and construct a supersymmetric field theory that resembles the Standard Model. We will cover D-branes, which are supersymmetric string solitonic 1 solutions. A Dp-brane is a membrane with p spatial dimensions (or p+1 spacetime dimensions). We will study Dp-branes, NS-branes, M-branes, small instantons, and their world-volume theories and interactions. We'd like to build up an understanding of quantum field theory and supersymmetric gauge theory in the world-volume of the brane, so that we can eventually make a connection to phenomenology.

Text, Lecture Notes, and Readings

There is no required textbook for this course. There are class notes and associated readings in the lecture notes section.

References for Mathematical Background:

Forms

Nakahara, Mikio. Geometry, Topology and Physics. 2nd ed. Philadelphia, PA: Institute of Physics Publishing, 2003. ISBN: 9780750306065.

Group Theory

Slansky, R. Group Theory for Unified Model Building. Physics Reports, Volume 79, Issue 1, p. 1-128.

Assignments and Exams

Problem sets will be due one week after they are assigned. There will be no final exam.

Grading

The course grade is based 100% on the problem sets.

Calendar