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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


Central Charge Formulas for W Bosons

Root Systems of Lie Algebras
10-11 BPS Objects Living on Branes



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 Dp 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 - Dp-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