Introduction to String Theory

Introduction to String Theory (Fall '20)


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. 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), barebones of conformal field theory, RNS superstring, simple string amplitudes, D-branes.

Special topics (roughly the last month or so) --- glimpses of: D-brane effective actions and gauge theory, compactification and Calabi-Yaus, string dualities, AdS/CFT.

Regular suggested assignments (incorporated into class).

Lec 1+2 (27/8): broad overview and context; lightcone quantization of bosonic string -- transverse modes, zpe, critical dimension. [P.ch.1] [W.ch.4, more details]

Lec 3-4 (3/9): lightcone quantization, quick recap; covariant strings -- classical stuff (mode expansions, energy momentum tensor constraints etc), quick overview of old covariant quantization and critical dimension again. [P.ch.1] [W ch.2, 3] [GSW.ch.2.1,2.3]

Lec 5-6 (10/9): old covariant quantization of bosonic strings, cont'd (in part using Ooguri's TASI 96 lectures) -- physical state condns, null states, comparing OCQ with LCQ, level-2 and critical dimension. Preview of the Polyakov path integral and gauge fixing. [P.ch.4.1] [W.ch.3] [GSW.ch.2.2], [P.ch.3.1-3.4]

Lec 7-8 (17/9): Polyakov path integral, gauge fixing --> X+bc conformal field theory. Lightning overview of bosonic strings in curved backgrounds and spacetime equations from 2d Weyl inv. [P.ch.3.1-3.4] [W.ch.3] [GSW.ch.3.1], [P.ch.3.7] [GSW.ch.3.4]

Lec 9-10 (24/9): 2-dim conformal field theory -- general properties following from conformal invariance in general dimensions; then specializing to 2-dims and infinite conformal symmetry. [P.ch.2] [W.ch.8]

Lec 11-12 (1/10): constraints of conformal invariance on 2- & 3-pt correlation functions; 2-dim massless scalars in complex coordinates, path integrals, normal ordered operators, OPEs. [di Francesco et al, ch.4,5] [P.ch.2]

Lec 13-14 (8/10): [mostly from P.ch.2] more on OPEs, massless scalars and the stress tensor; conformal symmetry and Ward identities; transformations of conformal fields and OPE with stress tensor; TT OPE, central terms, Schwarzian etc.

Lec 15-16 (15/10): more on conformal transformations and Ward identities (from W.ch.8, bit complementary and useful); radial ordering, cylinder vs plane, contour arguments and commutation relations; Virasoro algebra (P.ch.2 and W.ch.8).

Lec 17-18 (29/10):

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