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An Introduction to String Theory - UCB Mathematics

Preprint typeset in JHEP style - PAPER VERSIONR evised May 6, 2011An Introduction to String TheoryKevin WrayAbstract:This set of notes is based on the course Introduction to String Theory which was taught by Prof. Kostas Skenderis in the spring of 2009 at the Universityof Amsterdam. We have also drawn on some ideas from the booksString Theory andM- Theory (Becker, Becker and Schwarz), Introduction to String Theory (Polchinski), String Theory in a Nutshell(McMahon) andSuperstring Theory (Green, Schwarz andWitten), along with the lecture notes of David Tong, sometimes Motivation for String What is String Types of String Outline of the Manuscript92. The Bosonic String Classical Action for Point Classical Action for Relativistic Point Reparametrization invariance of Canonical Varying S0in an Arbitrary Background (Geodesic Equation) Generalization to The String Exercises243. Symmetries and Field Equations of the Bosonic Global Symmetries of the Bosonic String Theory Local Symmetries of the Bosonic String Theory Field Equations for the Polyakov Solving the Field Exercises424.

6.4.1 Constraints of Conformal Invariance in d Dimensions 87 6.5 Conformal Field Theories in 2 Dimensions 89 6.5.1 Constraints of Conformal Invariance in 2 Dimensions 90 6.6 Role of Conformal Field Theories in String Theory 92 6.7 Exercises 94 7. Radial Quantization and Operator Product Expansions 95 7.1 Radial Quantization 95

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