String theory and quantum gravity : proceedings of the Trieste Spring School, 23 April-1 May 1990 PDF
Preview String theory and quantum gravity : proceedings of the Trieste Spring School, 23 April-1 May 1990
- I <t: \ INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS '~e' INTERNATIONAL ATOMIC UNITEO NATIONS EDUCATIONAL. SCIENTIFIC 'J:Jf§ ENERGY AGENCY ANO CULTURAL ORGANIZATION of the Trieste Spring School ~roceedings . 23 Ap~il-·1 May ·l990 Eilited by . M. Gr;een .,,\b R. lengo S. Randjbar-Oaemi E. Sezgin lit.' Verlinde World Scientific STRITNHGE ORAYN D QUANTUGMR AVITY This page is intentionally left blank INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS I A\ ~ INTERNATIONAL ATOMIC UNITED NATIONS EDUCATIONAL, SCIENTIFIC ~...~.,.._, § ENERGY AGENCY AND CULTURAL ORGANIZATION ~ STRING THEORY AND QUANTUM GRAVITY Proceedings of the Trieste Spring School 23 April - 1 May 1990 Edited by M. Green R. lengo S. Randjbar-Daemi E. Sezgin H. Verlinde lb World Scientific ' ,,. Singapore • New Jersey • London • Hong Kong Publishbye d WorldSc ientifiPucb lishCoi.n g Pte.L td. P 0B ox1 28F,a rrer RoaSdin,g apore9 128 USAo ffice:68 1 HartweSlltre et,T eanecNkJ,0 7666 UK office:1 3L yntonM ead,T otteridgLoned,o n N208 DH Proceedings of theT riesteS prinSgc hool STRINGT HEORY AND QUANTUM GRAVITY Copyrig©h t199b1y W orldS cientifiPucb lishCoi.n gPte . Ltd. Alrli ghJsr eserveTdhis. b ooko,rpa rts thermaeyo nof.t b er eproduceidna nfyo rm orb yan y means,e lectroormen cihacn icalin,c ludingp hotocopyinrge,c ordoiran ngy informatiosnt oraandg er etr�syvsatle nowm known ort ob ei nventweidt,h oUl writtpeernm issifroomn thPeub lisher. ISBN 981-02-0372-1 l'rintienSd i ngapboyr JeB WP rint&e Brisn dePrtse L.t d. v PREFACE The 1990 Trieste Spring School covered a wide variety of topics of cur rent interest, all directly or indirectly related to String Theory and Quantum Gravity. The School was in fact perfectly timed because in the months before there had been remarkable progress in the understanding of two-dimensional quantum gravity and non-critical string theory. The solution of matrix models of random surfaces had provided an impressive amount of concrete results and had revealed surprising connections with integrable systems and topological field theory. These developments were discussed during the School in lectures by F. David and AI. Zamolodchikov who both gave a survey of the contin uum formulation of two-dimensional gravity (Liouville theory) as well as the discretized approach (matrix models). The lectures by E. and H. Verlinde cov ered aspects of two-dimensional conformal and topological field theory, with special attention to the relation between two-dimensional topological gravity and the one matrix model. The beautiful area of theoretical physics between conformal field theory and integrable lattice models was the topic of lectures by J .-B. Zuber and H. Saleur. Their lectures also covered some of the recent results on quantum groups and knot theory. The intriguing correspondence between conformal field theory, self-dual lattices and codes were discussed (among other things) by P. Goddard. H. Ooguri reported on very interesting progress made in col laboration with C. Vafa, on critical N =2 string theory and its connection with self-dual gravity in four-dimensional space with (2,2) signature. Finally, W. Fischler and L. Sussknid gave an exposition of some recent developments in four dimensional field theory and quantum gravity, including baryon produc tion at high temperatures in the standard model and baby universes. This page is intentionally left blank vii CONTENTS Preface v Integrable Lattice Models and Quantum Groups 1 H. Saleur and J.-B. Zuber Matrix Models and 2-D gravity 55 F. David Notes on Topological String Theory and 2D Quantum Gravity 91 R. Dijkgraa/, E. Verlinde and H. Verlinde Geometry of the N = 2 String Theory 157 H. Ooguri This page is intentionally left blank Integrable Lattice Models and Quantum Groups H. Saleur • and J.-B. Zuber Service de Physique Theorique de Saclay 1 F-91191 Gif-sur-Yvette cedex, France These lectures aim at introducing some basic algebraic concepts on lattice integrable mod els, in particular quantum groups, and to discuss some connections with knot theory and conformal field theories. The list of contents is: 1) Vertex models and Yang-Baxter equation 2) Quantum sl(2) algebra and the Yang-Baxter equation. 3) Uq sl(2) as a symmetry of statistical mechanical models. 4) Face models. 5) Face models attached to graphs. 6) Yang-Baxter equation, braid group and link polynomials. • (Address after May 15, 1990: Institute for Theoretical Physics, Santa Barbara, CA )3106) 1 Laboratoire de I' Institut de Recherche Fondamentale du Commissariat a l'Energie Uomique
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