This course is meant to serve as an introduction to some of the various facets of the subject that goes by the name of string theory, leading up to holography (AdS/CFT). The hope is that the course will equip the audience with some details on worldsheet strings as well as a roadmap of some of the various corners of this subject so one can then go follow up on some subarea in detail. [Unfortunately some subtopics will probably be left out altogether, apologies!]
Books (text+reference): the books on string theory by Polchinski (2 vols); Peter West ("Strings & Branes"); Green,Schwarz,Witten (2vols); Johnson; Kiritsis; Zwiebach, etc.
Course outline (broadly) --- relativistic string spectrum (lightcone gauge), string quantization (old covariant, path integral), aspects of 2-dim conformal field theory, RNS superstring, torus amplitude, D-branes.
Special topics (roughly the last month or so) --- glimpses of: D-brane effective actions and gauge theory (maybe compactification and Calabi-Yaus also), aspects of string dualities, AdS/CFT.
Regular suggested assignments (incorporated into class).
[See also previous versions of similar courses given in Fall '13 and Fall '20 + Spring '21.]
Lec 1+2 (9/1, 13/1): broad overview and context; lightcone quantization of bosonic string -- transverse modes, zpe, critical dimension. [P.ch.1] [W.ch.4] [GSW 2.1, 2.3]
Lec 3+4 (16/1, 20/1): covariant strings -- classical stuff (mode expansions, energy momentum tensor constraints etc), quick overview of old covariant quantization -- physical state condns, null states, comparing OCQ with LCQ, level-2 and critical dimension. [P.ch.1] [W ch.2, 3] [GSW.ch.2.1,2.3] (also Ooguri's TASI 96 lectures) [P.ch.4.1] [W.ch.3] [GSW.ch.2.2],
Preview of the Polyakov path integral and gauge fixing --> diffxWeyl [P.ch.3.1-3.4]
Lec 5-9 (23/1) (27/1) (30/1) (3/2) (10/2): 2-dim conformal field theory -- general properties following from conformal invariance in general dimensions; then specializing to 2-dims, complex coords etc, and infinite conformal symmetry; implications of conformal invariance for correlation functions. [di Francesco et al, ch.4,5] [ [P.ch.2] [W.ch.8]
[mostly from P.ch.2] 2-dim massless scalars, normal ordering, the stress tensor; contractions and the TT OPE; w- vs z-plane, radial quantization and commutators from OPEs; conformal symmetry and Ward identities; transformations of conformal fields and OPE with stress tensor; central terms, Schwarzian etc.
Lec 10 (13/2): "Why strings?" (big picture general lecture, in response to a question from a student)
Lec 11 (17/2): more on Virasoro and L0, L[n], L[-n] etc, and algebras for general primary operator mode expansion coefficients; radial quantization -- scalar mode expansions, operator commutation relations via contour/ope, conformal vs creation-annihilation normal ordering; state-operator correspondence. [P.ch.2 and W.ch.8]
Lec 12-13 (27/2, 03/3): Modular invariance and the 1-loop vacuum string amplitude (torus partition function); Torus as plane modulo lattice; fundamental domain of the torus; string regularization of potential UV divergence (vs point particle div). [P.ch.5 & 7]
Lec 14-18 (03/4, 07/4, 10/4, 17/4, 21/4): superstring (RNS) -- worldsheet fermions, NS/R boundary conditions, zpes and NS ground state lightcone spectrum to superstring critical dimension; the supercurrent and superconformal transformations, SCFTs. [P.ch.10]
superstrings, old covariant quantization; NS ground state spectrum. Ramond ground state: spinors in D=10, spinor products; the GSO projection, open superstring spectrum and the Type IIA and IIB string spectra. [mostly P.ch.10] [W.ch.7] [also Ooguri's TASI 96 lectures]
A quick look ahead -- IIA/IIB/11d supergravity; minimal coupling to RR gauge fields and D-branes, D3-brane stacks, SYM vs black 3-branes --> AdS/CFT duality..