Introduction to String Theory

Introduction to String Theory (Fall '13)

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); 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: broad overview and context; lightcone quantization of bosonic string. []

Lec 3: lightcone quantization cont'd; covariant strings (classical stuff). [] [,2.3] []

Lec 4+5: old covariant quantization of bosonic strings. [] [] []

Lec 6+7: Polyakov path integral --> X+bc conformal field theory. [] [] []

Lec 8+9: bosonic strings in curved backgrounds and spacetime equations from 2d Weyl inv. [] []; beginnings of 2d CFT [] [see also, Ginsparg lecs '91].

Lec 10+11: conformal invariance and 2d CFTs [ etc].

Lec 12+13: 2d CFTs cont'd [ etc].

Lec 14+15: 2d CFTs cont'd [ etc]; introduction to the closed string 1-loop amplitude, the torus and modular invariance [,7 etc].

Lec 16+17: modular invariance and UV finiteness of string 1-loop amplitude; glimpse of strings at finite temperature and the Hagedorn transition; superstring lightcone quantization (brief) and D=10 as critical dimension. [] [] []

Lec 18+19: superstrings, old covariant quantization; NS ground state spectrum. Ramond ground state: spinors in D=10, spinor products; the GSO projection and the Type IIA and IIB string spectra. []

Lec 20+21: recap of closed IIA/IIB superstring spectra; D=10 IIA and IIB supergravity effective actions (bosonic part), IIA sugra as KK-reduction of 11D sugra; reviewing the Reissner-Nordstrom black hole in Einstein-Maxwell theory, extremal limit, near horizon geometry; classical black brane solutions. [,14] (see also Kiritsis, Johnson; also Maldacena thesis 9607235, Peet TASI lecs, 0008241, etc)

Lec 22+23: snapshot of Type II compactification and Calabi-Yau spaces --> N=2 d=4 sugra; black branes cont'd; 3-branes and string perturbation theory limit (g_s-->0), rigid hypersurface with negligible gravitational backreaction, minimal coupling to RR gauge fields; IIA/B spectrum of p-branes; T-duality and D-branes. [,14,10], also Johnson, Kiritsis etc.

Lec 24+25: quick review of T-duality for open strings and D-branes; DBI-WZ action and low energy effective action; multiple D-branes, nonabelian super Yang-Mills theories and geometrizing the Higgs mechanism; noncommuting matrix coordinates for D-branes and a glimpse of the Myers dielectric effect; Bogomolnyi bounds, BPS point charges and the brane spike; string webs, brane prongs and dyon bound states; a snapshot of AdS/CFT. [,13,14] [Johnson] [Callan-Maldacena'97].

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