"Non perturbative String Theory 001.ps.gz" - читать интересную книгу автораhep-th/9802051 v2 15 Feb 1998 hep-th/9802051 An Introduction to Non-perturbative String Theory1 Ashoke Sen2 Mehta Research Institute of Mathematics and Mathematical Physics Chhatnag Road, Jhoosi, Allahabad 211019, INDIA Abstract In this review I discuss some basic aspects of non-perturbative string theory. The topics include test of duality symmetries based on the analysis of the low energy effective action and the spectrum of BPS states, relationship between different duality symmetries, an introduction to M- and F-theories, black hole entropy in string theory, and Matrix theory. 1Based on lectures given at the Isaac Newton Institute and the Department of Applied Mathematics and Theoretical Physics, University of Cambridge, UK. 2E-mail: [email protected] Contents 0 Introduction 3 1 A Brief Review of Perturbative String Theory 5 1.1 The spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.2 Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.3 Compactification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.1 Duality symmetries: Definition and examples . . . . . . . . . . . . . . . . . 16 2.2 Testing duality conjectures . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3 Analysis of Low Energy Effective Field Theory 21 3.1 Type I - SO(32) heterotic duality in D=10 . . . . . . . . . . . . . . . . . . 23 3.2 Self-duality of heterotic string theory on T 6 . . . . . . . . . . . . . . . . . 26 3.3 Duality between heterotic on T 4 and type IIA on K3 . . . . . . . . . . . . 30 3.4 SL(2,Z) self-duality of Type IIB in D=10 . . . . . . . . . . . . . . . . . . . 34 3.5 Other examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 4 Precision Test of Duality: Spectrum of BPS States 39 4.1 SL(2,Z) S-duality in heterotic on T 6 and multi-monopole moduli spaces . . 42 4.2 SL(2,Z) duality in type IIB on S1 and D-branes . . . . . . . . . . . . . . . 49 4.3 Massless solitons and tensionless strings . . . . . . . . . . . . . . . . . . . . 60 5 Interrelation Between Different Duality Conjectures 62 5.1 Combining non-perturbative and T- dualities . . . . . . . . . . . . . . . . . 62 5.2 Duality of dualities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 5.3 Fiberwise duality transformation . . . . . . . . . . . . . . . . . . . . . . . 64 5.4 Recovering higher dimensional dualities from lower dimensional ones . . . . 68 6 Duality in Theories with Less than Sixteen Supersymmetry Generators 70 6.1 Construction of dual pair of theories with eight supercharges . . . . . . . . 70 6.2 Test of duality conjectures involving theories with eight supercharges . . . 74 |
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