Introduction to String Theory

Institut fur Theoretische Physik, Universit at Heidelberg, 2012. — 177 p. Contents Literature Motivation and Overview Why do we study String Theory? The need for a quantum theory of gravity Programme The classical bosonic string The relativistic point particle The bosonic string action Oscillator expansions Quantisation of the bosonic string Old canonical quantisation Light-cone quantisation (LCQ) Modern covariant quantisation Conformal eld theory (CFT) Conformal invariance The conformal group in d 3 The conformal group in d = 2 Conformal elds and their OPE Conformal Ward-Takahashi identities and energy-momentum tensor State-operator correspondence, highest weight states, Verma modules Correlation functions in CFT Normal ordering and Wick's theorem Applications to String Theory String Interactions Perturbative Expansion Moduli space of Riemann surfaces The gauge xed S-matrix Tree-level amplitudes 1-loop amplitudes Strings on curved backgrounds Superstring theory The classical RNS action Super-conformal invariance Mode expansions: Ramond vs. Neveu-Schwarz Canonical quantisation and Super-Virasoro-Algebra Open string spectrum in light-cone quantisation (all NN) Closed string spectrum in LCQ The GSO projection: Type IIA and Type IIB