Abdalla, E., Abdalla, M.C.B., Dalmazi, D., Zadra, A.
1994, IX, 319 pp.
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The aim of this book is to bring together and compare two different approaches to the problem of the quantization of two-dimensional gravity and supergravity: we begin with the Liouville approach, which is formulated in the continuum two dimensionalspace-timeand makes extensive useofconformalfield theory techniques; the second approach is basedon a discretization oftwo-dimensionalrandom surfaces and described in terms ofmatrix models, where loop equations andlarge N methods play an important role. Over the last six years we have witnessed the interacting development of these different formulations. As if one model were a laboratory for its counterpart, one could test its ideas, conjectures, approximations and main results. Fromsuch exper iments welearned that each methodhas its own virtues: for instance, matrixmodels are excellent for higher genus surfaces and indeed they provide a non-perturbative definition of quantum gravity; on the other hand, the N = 2 supergravity theory misses a discrete formulation and, in this case, the continuum approach is more ad vanced. We hope this healthy "competition" between methods will continueimprov ing our understanding of the quantum gravity problem. Here lies the importance and usefulness of powerful alternative techniques.
Content Level »Research
Keywords »Gravity - Non-Critical Strings - Supersymmetry - conformal invariance - general quantum field theory - nonlinear equations - quantum field theory - string theory
Correlation Functions in the Bosonic Theory (Continuum Approach for Spherical Topology).- Hermitian Matrix Model.- Conformal Basis for Scaling Operators.- Correlation Functions for the N=1 Super Liouville Theory.- N=1 Super Eigenvalue Model.- Correlation Functions in N=2 Super Liouville Theory.- Final Remarks and Outlook.