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Physics - Quantum Physics | 2D-Gravity in Non-Critical Strings - Discrete and Continuum Approaches

2D-Gravity in Non-Critical Strings

Discrete and Continuum Approaches

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

Related subjects » Applied & Technical Physics - Astronomy, Observations and Techniques - Astrophysics and Astroparticles - Particle and Nuclear Physics - Quantum Physics - Theoretical, Mathematical & Computational Physics

Table of contents 

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.

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