Introduction to String Theory - ETH Z

1 Introduction to String TheoryLecture NotesETH Z urich, HS13 Prof. N. Beisert, Dr. J. Br odelc 2014 Niklas Beisert, Johannes Br odel, ETH ZurichThis document as well as its parts is protected by of any part in any form without prior writtenconsent of the author is permissible only for private,scientific and non-commercial Contents .. References ..61 Definition .. Motivation .. Some Conventions .. Relativistic Point Non-Relativistic Actions .. Worldline Action.

2 Polynomial Action .. Various Gauges .. Quantisation .. Interactions .. Conclusions .. Classical Bosonic Nambu Goto Action .. Polyakov Action .. Conformal Gauge .. Solution on the Light Cone .. Closed String Modes .. Hamiltonian Formalism .. String Canonical Quantisation .. Light Cone Quantisation .. String Spectrum .. Anomalies .. Covariant Quantisation .. Compactification and Kaluza Klein Modes .. Winding Modes.

3 T-Duality .. General Compactifications .. Open Strings and Neumann Boundary Conditions .. Solutions and Spectrum .. Dirichlet Boundary Conditions .. Multiple Branes .. Conformal Field Conformal Transformations .. Conformal Correlators .. Local Operators .. Operator Product Expansion .. Stress-Energy Tensor .. String Vertex Operators .. Veneziano Amplitude .. String Loops .. General Relativity Differential Geometry .. Riemannian Geometry.

4 General Relativity .. String Graviton Vertex Operator .. Curved Backgrounds .. Form Field and Dilaton .. Open Strings .. Two-Form Field of a String .. Supersymmetry .. Green Schwarz Superstring .. Ramond Neveu Schwarz Superstring .. Branes .. Other Superstrings .. Effective Field Effective Action and Compactifications .. Open Strings .. Closed Strings .. Relations Between String Amplitudes .. String T-Duality.

5 Strong/Weak Coupling Duality: S-Duality .. Strong Coupling Limits .. M- Theory .. String Theory and the Standard The Real World .. Geometry of Toroidal Manifolds and Orbifolds .. Calabi Yau Compactification ofD= 10 Supergravity .. String Theory as a Phenomenological Model .. AdS/CFT Stack of D3-Branes .. Anti-de Sitter Geometry .. 4 Super Yang Mills .. Tests .. to String TheoryChapter 0 ETH Z urich, HS13 Prof. N. Beisert, Dr. J. Br odel22.

6 12. 20130 OverviewString Theory is an attempt to quantise gravity and unite it with the otherfundamental forces of nature. It combines many interesting topics of (quantum)field Theory in two and higher dimensions. This course gives an Introduction to thebasics of String Contents1. Introduction (1 lecture)2. Relativistic Point Particle(2 lectures)3. Classical Bosonic String (3 lectures)4. String Quantisation(4 lectures)5. Compactification and T-Duality(2 lectures)6. Open Strings and D-Branes(2 lectures)7.

7 Conformal Field Theory (4 lectures)8. String Scattering(2 lectures)9. General Relativity Basics(2 lectures)10. String Backgrounds(3 lectures)11. Superstrings and Supersymmetry(4 lectures)12. Effective Field Theory (3 lectures)13. String Dualities(3 lectures)14. String Theory and the Standard Model(2 lectures)15. AdS/CFT Correspondence(2 lectures)Indicated are the approximate number of 45-minute lectures. Altogether, thecourse consists of 39 ReferencesThere are many text books and lecture notes on String Theory .

8 Here is a selectionof well-known ones: classic: M. Green, Schwarz and E. Witten, Superstring Theory (2volumes), Cambridge University Press (1988) alternative: D. L ust, S. Theisen, Lectures on String Theory , Springer (1989). new edition: R. Blumenhagen, D. L ust, S. Theisen, Basic Concepts of StringTheory , Springer (2012). standard: J. Polchinski, String Theory (2 volumes), Cambridge UniversityPress (1998) basic: B. Zwiebach, A First Course in String Theory , Cambridge UniversityPress (2004/2009)6 recent: K.

9 Becker, M. Becker, Schwarz, String Theory and M- Theory : AModern Introduction , Cambridge University Press (2007) online: D. Tong, String Theory , lecture notes , ..7 Introduction to String TheoryChapter 1 ETH Z urich, HS13 Prof. N. Beisert, Dr. J. Br odel22. 12. 20131 DefinitionString Theory describes the mechanics of one-dimensional extended objects in anambient space.( )Some features: Strings have tension:( ) Strings have no inner structure:but not( ) Several pieces of String can interact: ( ) Strings can be classical or quantum:vs.

10 ( ) Strings can be open or closed:vs.( ) MotivationWhy study strings?Extended know a lot about the mechanics of point particles. It isnatural to study strings next. Or even higher-dimensional extended objects likemembranes..particlestringmembrane( ) objects are snapshots at fixed timet. Introduce the worldvolume as thevolume of spacetime occupied by the object:worldlineworldsheetworldvolume( )The worldsheet of a String is two-dimensional. In fact, there is a great similaritybetween strings and static soap Theory offers a solution to the problem of quantumgravity (QG).