This is a second course in String Theory (following the Introductory course last sem). I will cover specific topics, e.g. supergravity, branes in sugra, D-branes etc, and eventually AdS/CFT. [Unfortunately various subtopics will be left out altogether]
Books (text+reference): the books on string theory by Polchinski (2 vols); Peter West ("Strings & Branes"); Blumenhagen,Lust,Theisen; Green,Schwarz,Witten (2vols); Johnson; Kiritsis; Zwiebach, etc.
Also certain specific papers. And earlier notes of mine from previous courses.
Regular suggested assignments (incorporated into class).
Lec 0 (7/1/21): organizational. Each lec will be about 2 hrs (sometimes more!), comprising effectively 2 lectures.
Lec 1-2 (14/1): Kaluza-Klein compactification of 5d GR to 4d GR+EM+scalar; 11-dim supergravity compactification to 10d IIA; Reissner-Nordstrom black hole in Einstein-Maxwell theory, extremality etc; black M2-brane in 11-dim sugra; [P.ch.8] [P.ch.12] [W.ch.13];
Lec 3-4 (21/1): strings on a torus, modular invariance and theta functions; modular invariance of Type II superstrings; brief overview of bosonization; [P.ch.7] [P.ch.10];
Lec 5-6 (28/1): student presentations on constructing supergravity theories [W.ch.13]; very brief glimpse of black hole thermodynamics.
Lec 7-8 (04/2): open string mode expansions with NN,DD,ND,DN boundary conditions and in CFT language (on upper half-plane); D-boundary conditions as describing open strings ending on D-branes; T-duality of closed strings, extra massless charged states and enhanced gauge symmetries at special radii; T-duality for open strings, emergence of a single D-brane; (multiple D-branes, later) [BLT.ch.2 & 4] [W.ch.15] [P.ch.8];
Lec 9-10 (11/2): student presentations on supergravity cont'd [W.ch.13].
Lec 11-12 (18/2): student presentations on supergravity (dim'nal reduction) cont'd [W.ch.13].
Lec 13-14 (25/2): open strings and Chan-Paton factors --> T-duality with nontrivial Wilson lines --> multiple D-branes; enhanced gauge symmetry and geometrizing the Higgs mechanism; T-duality along D-brane w-volume; open string fluctuations and D-brane dynamics --> DBI action --> static gauge and YM+scalars action [P.ch.8].
Lec 15-16 (04/3): student presentations -- deriving brane solutions in supergravity [W.ch.13.8.1].
Lec 17-18 (11/3): student presentations -- brane solutions in 11d and Type II supergravity, brane charges and susy algebra [W.ch.13.8].
Lec 19-20 (18/3): (D-branes cont'd) T-duality for closed superstrings and mapping IIA/IIB RR fields and D-branes; D-brane DBI action cont'd -- expanding to obtain SYM as low energy effective field theory on D-branes; WZ couplings to RR background fields (e.g. axion --> theta angle); [Xa,Xb]^2 term and noncommuting matrices for D-branes; glimpse of Myers dielectric effect; Bogomolnyi bounds, BPS point charges and the Callan-Maldacena brane spike. [P.ch.13] [earlier notes of mine].
Lec 21-22 (25/3): recap T-duality IIA/IIB; SL(2,Z) duality of IIB strings; strong coupling limit of IIA strings and M-theory; glimpse of the web of string dualities; D3-brane stacks, scattering of closed strings and the "experimental findings" on absorption cross-sections; the physical decoupling arguments (low energy, large N etc) --> AdS/CFT; brief summary of symmetries etc; more general AdS x X backgrounds from D3-branes at singularities etc; M2/M5-branes and AdS/CFT. [P.ch.12, 14] [my notes].
Lec 23-24 (01/4) [longish! ~2hr20min]: essentials of AdS/CFT; basic geometry of AdS and symmetries; scale-radius duality; scalar field probes and a detailed discussion of momentum space 2-pt correlation functions via the (Euclidean) GKPW dictionary, removing divergences via local counterterms; energy-momentum tensor 2pt fn and D3/M2/M5 CFT central charges holographically; snapshot of holographic stress tensor and holographic renormalization; holographic entanglement entropy (snapshot in QM/QFT, minimal surfaces & RT formulation, simple examples). [my notes]