Intro to String Theory - G. terHooft

Intro to String Theory - G. terHooft - INTRODUCTION TO...

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Unformatted text preview: INTRODUCTION TO STRING THEORY * version 14-05-04 Gerard t Hooft Institute for Theoretical Physics Utrecht University, Leuvenlaan 4 3584 CC Utrecht, the Netherlands and Spinoza Institute Postbox 80.195 3508 TD Utrecht, the Netherlands e-mail: g.thooft@phys.uu.nl internet: http://www.phys.uu.nl/~thooft/ Contents 1 Strings in QCD. 4 1.1 The linear trajectories. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2 The Veneziano formula. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2 The classical string. 7 3 Open and closed strings. 11 3.1 The Open string. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.2 The closed string. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 3.3 Solutions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 3.3.1 The open string. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 3.3.2 The closed string. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 3.4 The light-cone gauge. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3.5 Constraints. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3.5.1 for open strings: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 * Lecture notes 2003 and 2004 1 3.5.2 for closed strings: . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 3.6 Energy, momentum, angular momentum. . . . . . . . . . . . . . . . . . . . 17 4 Quantization. 18 4.1 Commutation rules. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 4.2 The constraints in the quantum theory. . . . . . . . . . . . . . . . . . . . . 19 4.3 The Virasoro Algebra. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 4.4 Quantization of the closed string . . . . . . . . . . . . . . . . . . . . . . . 23 4.5 The closed string spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 5 Lorentz invariance. 25 6 Interactions and vertex operators. 27 7 BRST quantization. 31 8 The Polyakov path integral. Interactions with closed strings. 34 8.1 The energy-momentum tensor for the ghost fields. . . . . . . . . . . . . . . 36 9 T-Duality. 38 9.1 Compactifying closed string theory on a circle. . . . . . . . . . . . . . . . . 39 9.2 T-duality of closed strings. . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 9.3 T-duality for open strings. . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 9.4 Multiple branes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 9.5 Phase factors and non-coinciding D-branes. . . . . . . . . . . . . . . . . . 42 10 Complex coordinates. 43 11 Fermions in strings. 45 11.1 Spinning point particles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 11.2 The fermionic Lagrangian. . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 11.3 Boundary conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 11.4 Anticommutation rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5111....
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This note was uploaded on 09/29/2011 for the course PHYS 222 taught by Professor Wade during the Spring '09 term at Edmonds Community College.

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Intro to String Theory - G. terHooft - INTRODUCTION TO...

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