Hanany, Amihay, 8.871 Selected Topics in Theoretical Particle Physics: Branes and Gauge Theory Dynamics, Fall 2004. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed 09 Jul, 2010). License: Creative Commons BY-NC-SA

Brane tiling for the complex cone over the third del-Pezzo surface. Red lines are NS branes, faces, are D5 branes. The gauge theory consists of 6 gauge groups, 14 fields, and 8 interaction terms. (Image by Prof. Amihay Hanany and Madeleine Sheldon-Dante.)

This course features lecture notes and assignments.

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 D*p*-brane is a membrane with *p* spatial dimensions (or *p+*1 spacetime dimensions). We will study D*p*-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

Course calendar.
SES # |
TOPICS |

1 |
Introduction to Branes
Branes Ending on Branes
5 Superstring Theories, 11d Supergravity |

2-3 |
Central Charges in the Supersymmetry Algebra
Branes in Type II Theories
Dualities in String Theory
Tensions of Branes |

4-5 |
Supergravity in Various Dimensions - 32 Supercharges
Scalar Manifolds in Various Dimensions
Cosmic Strings |

6-7 |
u-dualities and Representations of *p*-forms
Electric and Magnetic Excitations on Branes
SYM Actions in Various Dimensions
Higgs Mechanism - Adjoint Representation |

8-9 |
Brane Realization of Classical Groups for Theories with 16 Supercharges
McKay Correspondence
Orientifolds
Central Charge Formulas for W Bosons
Root Systems of Lie Algebras |

10-11 |
BPS Objects Living on Branes
Instantons
Monopoles
Brane Realization of E_n Gauge Theories
E_n Representation Theory, Root Systems
Supergravity Multiplets - 16 Supercharges, Vector Multiplets and Tensor Multiplets
Gravitational Anomalies |

12-13 |
Enhanced Gauge Groups in Type I'
W Bosons and Root Systems
O8^{∧} Plane
Montonen Olive Duality and SL(2,Z), Brane Picture in Type IIB
Strong Coupling Phenomena in N=8 SYM in 3d and its Brane Realization
Orientifolds in Compact Backgrounds
5d SYM with 16 Supercharges and (0,2) Theories in 6d |

14-15 |
Magnetic Monopoles in Type I'
SL(2,Z) Duality and N=4 SYM on a Circle
UV Completion of 5d SYM with 16 Supercharges - D4 Brane Story
Splitting of O3 Planes |

16-17 |
Anomalies in 6d
3d Gauge Theories with 16 Supercharges
Theories with 8 Supercharges - Various Supermultiplets |

18 |
Theories with 8 Supercharges
Higgs Branch - Moduli Space of Instantons
Dual Coxeter Numbers and the Moduli Space of Instantons
Matter Content for D*p* Branes on O(*p*+4) planes
Moduli Space of Instantons - ADHM Construction |

19-20 |
Higgs Branch and the Moduli Space of Instantons - Classical Groups A, B, C, D
E_n Instantons
String Coupling Equation and Beta Function of Supersymmetric Gauge Theories
Vacuum Structure of Supersymmetric Gauge Theories with 8 Supercharges - Brane Picture
D Branes near Orientifold Planes
D4 Branes and 5d BPS States |

21 |
Brane Intervals - Hanany Witten Brane Configurations |

22-23 |
The String Coupling and Vector Multiplets
Effective Gauge Coupling at One Loop - D*p*-D(*p*+4) System
Asymptotically Free Gauge Theories with 8 Supercharges and D Brane Realization |

24-25 |
Mirror Symmetry in 3 Dimensions
Five Dimensional Fixed Points and their Low Energy Gauge Theory Limits
Brane Creation - The Hanany Witten Effect
Continuation Past Infinite Coupling |