Teaching

Spring/Summer 2018

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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)

Lecture 3 [March 13, 2018]:
3.0 Recap Lecture 2
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

Lecture 4 [March 15, 2018]:
4.0 Recap Lecture 3
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]

Lecture 10 [April 10, 2018]:
10.0 Recap Lecture 9
10.1 Comments about Basic Interaction Terms
10.2 Gauge Invariance
10.3 Towards the Worldsheet Action
10.4 Preview of new term in the action

Lecture 11 [April 12, 2018]:
11.0 Recap Lecture 10
11.1 Two Branes approaching each other
11.2 The Chern-Simons Term

Lecture 12 [April 17, 2018]:
12.0 Recap Lecture 11
12.1 Electromagnetic Duality on a Brane
12.2 Examples of Branes ending on Branes

Lecture 13 [April 19, 2018]:
13.0 Recap Lecture 12
13.1 D2 on D4
13.2 F1 on D1
13.3 D5 on NS5
13.4 IIB and SL(2,Z)

Lecture 14 [April 24, 2018]:
14.0 Recap Lecture 13
14.1 The Theory on a Dp-Brane
14.2 Tension of a String and Couplings
14.3 S-duality

Lecture 15 [April 26, 2018]:
15.0 Recap Lecture 14
15.1 Dimensional Reduction Revisited
15.2 S1 Compactification: M to IIA
15.3 Momentum Modes and KK Monopoles
15.4 M-Theory on 2-Torus

May 1 Week Holiday [May 1 & 3, 2018]

Lecture 16 [May 8, 2018]:
16.0 Recap Lecture 15
16.1 M-Theory on T2 vs IIA/IIB on S1
16.2 T-duality
16.3 S-duality, T-duality and U-duality

Lecture 17 [May 10, 2018]:
17.0 Recap Lecture 16
17.1 Duality Chains and Brane Configurations
17.2 Revisiting the Worldvolume Theory on a D-Brane
17.3 Dp on Dp+2 and Dp on NS5
17.4 Vector and Hypermultiplets

Lecture 18 [May 15, 2018]:
18.0 Recap Lecture 17
18.1 Chan-Paton Factors
18.2 A NS5, D5 and D3 configuration
18.3 The Field Theory on the D3-brane

Lecture 19 [May 17, 2018]:
19.0 Recap Lecture 18
19.1 Vector and Hypermultiplets in 3d N=4
19.2 Brane Singularities
19.3 The Coulomb Branch and Magnetic Monopoles in 3d N=4

Lecture 20 [May 18, 2018 – extra lecture]:
20.0 Recap Lecture 19
20.1 The Construction of the 3d N=4 Coulomb Branch
20.2 Special Examples of the Coulomb Branch
20.3 A Hypermultiplet Paradox?

Lecture 21 [May 22, 2018]:
21.0 Recap Lecture 20
21.1 Hanany-Witten Transitions
21.2 Linking Numbers for 5-Branes
21.3 Linking Number Properties

Lecture 22 [May 24, 2018]:
22.0 Recap Lecture 21
22.1 Multiple Branes and Hanany-Witten Transitions
22.2 Linking Numbers and Partitions
22.3 Gaiotto-Witten Theories
22.4 Mirror Symmetry and Partitions

Lecture 23 [May 29, 2018]:
23.0 Recap Lecture 22
23.1 Conditions on Partitions and Non-Supersymmetric Theories
23.2 Higgs and Coulomb Branches of 3d N=4 Theories
23.3 Kraft-Procesi Transitions and Hasse Diagrams

Lecture 24 [May 31, 2018]:
24.0

Lecture 25 [June 1, 2018]:
25.0

Lecture 26 [June 5, 2018]:
26.0

Lecture 27 [June 7, 2018]:
27.0

Lecture 28 [June 8, 2018]:
28.0

Fin