The material below was provided to the students as class notes and associated readings.
SES #  TOPICS  NOTES AND REFERENCES 

1 
Introduction to Branes
Branes Ending on Branes 5 Superstring Theories, 11d Supergravity 
For today’s lecture, we have the following references:
 Open pBranes (Strominger) 
23 
Central Charges in the Supersymmetry Algebra
Branes in Type II Theories Dualities in String Theory Tensions of Branes 
Weinberg, Steven. The Quantum Theory of Fields. Vol. 3. New York, NY: Cambridge University Press, 19952000. ISBN: 9780521660006. A good reference for Supersymmetry algebras in higher dimensions can be found in chapter 32 of Weinberg’s book, The Quantum Theory of Fields (Vol. 3). In particular see 32.2 for the massless supermultiplets. The central extension to the supersymmetry algebra was first discussed in a paper by Witten Olive. The discussion we had today is a (straightforward) generalization of this paper. One replaces particles by branes and generalizes the number of spacetime dimensions. The central extension for a pbrane becomes a pform in the supersymmetry algebra instead of a 0form for a particle. A treatment of the central charge for 11d supergravity can be found in MTheory from its Super algebra (Townsend). (PDF) A derivation of the BPS bound which is the generalization of the Witten Olive computation can be found. And, Some Relationships Between Dualities in String Theory (Aspinwall). 
45 
Supergravity in Various Dimensions  32 Supercharges
Scalar Manifolds in Various Dimensions Cosmic Strings 
For collected works on supergravity in various dimensions see:
Salam, A., and E. Sezgin, eds. Supergravity In Diverse Dimensions. NorthHolland: World Scientific, 1989. For a discussion on scalar manifolds in various dimensions see for example Hull and Townsend. 
67 
udualities and Representations of pforms
Electric and Magnetic Excitations on Branes SYM Actions in Various Dimensions Higgs Mechanism  Adjoint Representation 
A nice treatment of anomalies in various dimensions can be found in the review paper of AlvarezGaume and Ginsparg.
In this paper there is a topological interpretation of the anomalies in terms of some index theorems. The 2 dimensional extension of the manifold for which the anomaly in calculated is described in section 3 where this 2 dimensional extension turns out to be a 2sphere. A summary of the ideas can be found in section 4. This reference answers in great detail all questions which were asked today in class about the derivation of the anomaly in even dimensions. 
89 
Brane Realization of Classical Groups for Theories with 16 Supercharges
McKay Correspondence Orientifolds Central Charge Formulas for W Bosons Root Systems of Lie Algebras 
A good review of string dualities can be found in the paper of lectures on Superstring and M Theory Dualities (Schwarz).
The next lecture, will be focused on the brane realization of the classical groups A, B, C, D for theories with 16 supercharges. We will learn for the first time in the course the deep connection between geometry and algebra as realized by the branes. We will cover orientifolds on their various types and learn about central charge formulas for W bosons and their relation to the root systems of the lie algebras. 
1011 
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 
In Lec #10, we will go over the BPS objects on the worldvolume of various branes. For gauge theories (which as is familiar by now live on D branes) these include the instanton and the ’t Hooft Polyakov monopole.
Next, we will discuss compact spacetimes with orientifolds and learn about the brane realization of E_n gauge theories. This will be the first nonperturbative dynamical result which can not be verified by the usual methods in perturbation theory. These are two possible references for learning about monopoles and instantons: Cheng, TaPei, and LingFong Li. Gauge Theory of Elementary Particle Physics. Oxford, NY [Oxfordshire]: Clarendon Press; New York, NY: Oxford University Press, 1984. ISBN: 9780198519560, 9780198519614. (Paperback.) Weinberg, Steven. The Quantum Theory of Fields. Vol. 2. New York, NY: Cambridge University Press, 1996. ISBN: 9780521550024. Another useful reference for the classical monopole solutions can be found in the paper by Gibbons and Manton. Polchinski, Joseph Gerard. String Theory. Vol. 1. Cambridge, UK; New York, NY: Cambridge University Press, 1998, p. 278. ISBN: 9780521633031. (Hardcover.) 
1213 
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 

1415 
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 
A good exposition of the duality between Type I’ superstring and the Heterotic string in 9 dimensions can be found in the paper String Creation and HeteroticType I’ Duality (Bergman, Gaberdiel and Lifschytz). 
1617 
Anomalies in 6d
3d Gauge Theories with 16 Supercharges Theories with 8 Supercharges  Various Supermultiplets 
A useful summary of supersymmetry multiplets and their properties can be found in Vadim Kaplunovsky’s notes. 
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 
In Lec #18, we continue to look at theories with 8 supercharges and will discuss the Higgs branch and its relation to the moduli space of instantons. 
1920 
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 
Read Lecture Note 3 (PDF) (Courtesy of Megha Padi. Used with permission.)
In Lec #19, we continue to look at the relation between the Higgs branch and the moduli space of instantons and extend the discussion to the classical groups: A_n, B_n, C_n, D_n. We will also learn about some aspects of the moduli space of E_n instantons. If time allows we will discuss the relation between the string coupling equation of motion and the beta function of supersymmetric gauge theories. 
21  Brane Intervals  Hanany Witten Brane Configurations  A source for the dual coxeter number of various groups can be found for example in Instantons and Magnetic Monopoles on _R__{3} × _S__{1} with Arbitrary Simple Gauge Groups (Lee). 
2223 
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 
In Lec #22, we will start looking at brane configurations involving D branes bounded by NS5branes  Brane Intervals.
A source for supermultiplets of (2,1) supersymmetry can be found in: Strathdee, J. (ICTP, Trieste), IC86/94, May 1986. “Extended Poincare Supersymmetry.” Int J Mod Phys A2, no. 273 (1987): 40. 
2425 
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 
For an M theory realization of Mirror Symmetry in 3 dimensions see Porrati and Zaffaroni.
For (p,q) Webs and their application to five dimensional fixed points see Aharony, Hanany, and Kol. 