Ebook: 2D-Gravity in Non-Critical Strings: Discrete and Continuum Approaches

This book contains a survey of the use of the Liouville (and super-Liouville) equation in (super)string theory outside the critical dimension, and of the complementary approach based on the discretized space-time, known as the matrix model approach. Supersymmetry is given particular attention, both in the continuum formulation, by means of the Liouville equation, and through the consideration of the super-eigenvalue problem. The methods presented here are important in a large number of complex problems, e.g. random surfaces, 2-D gravity and large-N quantum chromodynamics. The comparison of different methods in the study of such problems permits a cross-evaluation of the results when both methods are applicable and new predictions when only one of the methods may be used.

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This book contains a survey of the use of the Liouville (and super-Liouville) equation in (super)string theory outside the critical dimension, and of the complementary approach based on the discretized space-time, known as the matrix model approach. Supersymmetry is given particular attention, both in the continuum formulation, by means of the Liouville equation, and through the consideration of the super-eigenvalue problem. The methods presented here are important in a large number of complex problems, e.g. random surfaces, 2-D gravity and large-N quantum chromodynamics. The comparison of different methods in the study of such problems permits a cross-evaluation of the results when both methods are applicable and new predictions when only one of the methods may be used.
Content:
Front Matter....Pages i-ix
Introduction....Pages 1-29
Correlation Functions in the Bosonic Theory (Continuum Approach for Spherical Topology)....Pages 31-71
Hermitian Matrix Model....Pages 73-104
Conformal Basis for Scaling Operators....Pages 105-121
Correlation Functions for the N=1 Super Liouville Theory....Pages 123-150
N=1 Super Eigenvalue Model....Pages 151-200
Correlation Functions in N=2 Super Liouville Theory....Pages 201-212
Final Remarks and Outlook....Pages 213-242
Back Matter....Pages 243-319

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This book contains a survey of the use of the Liouville (and super-Liouville) equation in (super)string theory outside the critical dimension, and of the complementary approach based on the discretized space-time, known as the matrix model approach. Supersymmetry is given particular attention, both in the continuum formulation, by means of the Liouville equation, and through the consideration of the super-eigenvalue problem. The methods presented here are important in a large number of complex problems, e.g. random surfaces, 2-D gravity and large-N quantum chromodynamics. The comparison of different methods in the study of such problems permits a cross-evaluation of the results when both methods are applicable and new predictions when only one of the methods may be used.
Content:
Front Matter....Pages i-ix
Introduction....Pages 1-29
Correlation Functions in the Bosonic Theory (Continuum Approach for Spherical Topology)....Pages 31-71
Hermitian Matrix Model....Pages 73-104
Conformal Basis for Scaling Operators....Pages 105-121
Correlation Functions for the N=1 Super Liouville Theory....Pages 123-150
N=1 Super Eigenvalue Model....Pages 151-200
Correlation Functions in N=2 Super Liouville Theory....Pages 201-212
Final Remarks and Outlook....Pages 213-242
Back Matter....Pages 243-319
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