Download PDF by Elcio Abdalla: 2D-Gravity in Non-Critical Strings: Discrete and Continuum

By Elcio Abdalla

ISBN-10: 3540578056

ISBN-13: 9783540578055

This ebook incorporates a survey of using the Liouville (and super-Liouville) equation in (super)string concept outdoor the serious measurement, and of the complementary method in accordance with the discretized space-time, referred to as the matrix version procedure. Supersymmetry is given specific consciousness, either within the continuum formula, by way of the Liouville equation, and during the glory of the super-eigenvalue challenge. The tools offered listed below are vital in various advanced difficulties, e.g. random surfaces, 2-D gravity and large-N quantum chromodynamics. The comparability of other equipment within the research of such difficulties allows a cross-evaluation of the consequences while either equipment are acceptable and new predictions whilst just one of the equipment can be used.

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Additional resources for 2D-Gravity in Non-Critical Strings: Discrete and Continuum Approaches (Planetology)

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56). 155) from where we have the central charge c'" = 1 + 3Q2 j since we have Q= Ctot J25;C . 156) Critical exponents of the theory may be computed as follows. 157) defining the string susceptibility68 'Yh. 165) The above result, obtained by standard quantum field methods in the light-cone gauge, as well as by simple manipulations of the partition function in the conformal gauge, will be generalized for the expression of correlation functions involving vertex operators dressed by gravity in the continuum formulation of non-critical strings.

84]. 151) we find two critical values for c, the lowest ones being c = 1 for N = 0, and c = for N = 1. Below such points, a formulation of the theory in terms of vertex operators dressed by the Liouville (resp. later super Liouville) fields make sense. In the present Chapter we shall deal with the formulation of the bosonic case. The results are very rewarding. Even before comparing to the matrix models results, namely staying in the framework of the theory in the continuum formulation we may analyse, as an example, the spectrum of intermediate states.

22) At this point we use the zero mode technique. 10) from last section for the partition function on the sphere. e. 29) where the factor -Q/ 0+ is called the gravitational scaling of the partition function Z. In other words we can associate the factor jl-Q/a+ with the measure of the path integral. 30) We conclude that the gravitational scaling of 0, is -{3,/0+. These definitions will be useful later for a comparison with matrix model results. 26). We shall hold a positive attitude towards the singularity represented by r( -s), not restricting to correlation functions for fixed areas, putting aside for a while the existence of the singularity and proceeding with the calculation.

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2D-Gravity in Non-Critical Strings: Discrete and Continuum Approaches (Planetology) by Elcio Abdalla

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