**Spring/Summer 2018**

*YMSC Graduate Course*

**Brane Dynamics and Supersymmetric Gauge Theories**

This course is an introduction to branes in string theory and how they give rise to supersymmetric gauge theories in various dimensions. We will first cover the classification of different types of branes that arise in string theory and the bound states they form. We will then move on to the brane realizations of supersymmetric gauge theories in 2,3,4,5 and 6 dimensions. While doing so, we will explore how gauge theory phenomena such as dualities arise in terms of branes and how brane dynamics gives a powerful geometrical interpretation of such gauge theory phenomena. This course is intended to be a pedagogical introduction to the topic of branes in string theory with examples taken from modern developments in string theory, including topics like mirror symmetry and the Higgs and Coulomb branch of N=4 theories, branes at Calabi-Yau singularities and recent applications of Hanany-Witten brane setups.

*Prerequisite:*

Quantum Field Theory, Supersymmetry, Representation Theory

*Confirmed Schedule:*

Tuesdays and Thursdays, 17:00-18:40

March 6 – June 14, 2018

*Location:*

Yau Mathematical Sciences Center, Tsinghua University,

Conference Room 1, Jin Chun Yuan West Building

*Announcement:
http://ymsc.tsinghua.edu.cn/sjcontent.asp?id=1056*

*
Lecture 1 [March 6, 2018]:
*1.0 Why String Theory?

1.1 Strings & Branes

1.2 Spacetime Revisited

1.3 Symmetries & Spacetime

1.4 SO(8), D4

* Lecture 2 [March 8, 2018]:
*2.0 Recap Lecture 1

2.1 Representation Theory Revisited: SU(n) & SO(2n) Irreps, Characters

2.2 Supersymmetry & Chirality

2.3 10d Massless Supergravity Multiplets

2.4 10d SO(8) vs 11d SO(9)

*3.0 Recap Lecture 2*

**Lecture 3 [March 13, 2018]:**3.1 Representation Theory Revisited: SU(2n+1) Irreps, Characters

3.1 Dimensional Reduction & Branching Rules

3.2 What about d<10?

3.3 Maxwell’s Equations Revisited

*4.0 Recap Lecture 3*

**Lecture 4 [March 15, 2018]:**

4.1 Rewriting Maxwell’s Equations

4.2 Brane Spectroscopy (M, IIA, IIB)

* Lecture 5 [March 20, 2018]:*5.0 Recap Lecture 4

5.1 Electromagnetic Duality

5.2 The Vacuum and Moduli Spaces

5.3 Strings on Branes

5.4 Gauss’ Law

5.5 Towards Branes ending on Branes

* Lecture 6 [March 22, 2018]:*6.0 Recap Lecture 5

6.1 D-Branes and Magnetically Charged Objects

6.2 Vector Multiplets

6.3 Symmetries and Symmetry Breaking under a D-Brane

6.4 M2 ending on M5

* Lecture 7 [March 27, 2018]:*7.0 Recap Lecture 6

7.1 M2 on M5 and Electromagnetic Duality

* Lecture 8 [March 29, 2018]:*8.0 Recap Lecture 7

8.1 NS5-Branes

8.2 Multiplets in 5d

8.3 NS5- and D5-Branes

* Lecture 9 [April 3, 2018]:*9.0 Recap Lecture 8

9.1 Counting Supersymmetries

9.2 Multiplets and Supersymmetry

9.3 The Tensor Multiplet and M-Theory

9.4 Towards Actions

**Qingming Festival (Tomb-Sweeping Holiday) [April 5, 2018]**