By Elcio Abdalla
This ebook includes a survey of using the Liouville (and super-Liouville) equation in (super)string conception open air the severe size, and of the complementary technique in accordance with the discretized space-time, referred to as the matrix version strategy. Supersymmetry is given specific cognizance, either within the continuum formula, via the Liouville equation, and during the honour of the super-eigenvalue challenge. The tools offered listed below are vital in a number of complicated difficulties, e.g. random surfaces, 2-D gravity and large-N quantum chromodynamics. The comparability of alternative tools within the research of such difficulties allows a cross-evaluation of the implications whilst either tools are appropriate and new predictions whilst just one of the tools can be used.
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Additional info for 2D-Gravity in Non-Critical Strings: Discrete and Continuum Approaches (Planetology)
100b) - L (n, ... TkNTk=O) = [-2Ia N N Ik, - aol- (2 -1)(1 ,=1 +1 2a :")] (Tk,'" T kN ) . 119) For N = 4 this expression suggests the diagrammatic picture of Fig. 2. The contribution Ag PI is a contact term. We complete now As, which is known in the given kinematic region as before. + + Fig. 2: Contributions to the five point function. The strategy to extend As to other kinematic regions is first to compute the reducible diagrams in Fig. £ = 1); iii) each four legs vertex implies a factor A1 PI = -t(1 + ta:"), and finally iv) the momentum is conserved through any vertex.
Orr') = HO;r' - 20 00 rr ,). 40) for r, = r: 00 = [2q(q+1)]-1/2 and p' = (q+1)/q. ) are not important. Integrating out the zero mode cPo, Dotsenko obtained, besides the usual cosmological term to the power of s, a second term to the power s. 47b) 40 Although such a trick might a priori not be justified, the final result for the ratios of correlation functions does not seem to depend on the details of the continuation in s or s. 48) with the dressed tachyonic operator given by T k for the Liouville and matter fields written as = J d 2 zyge'kX +M and the action As before we have Q = 2}2 + a6; a± = -~ ± laol; moreover, a+a_ = 2.
In the previous Chapter we have reviewed several pieces of works dealing with the quantization of gravity; in the light-cone gauge it was possible to compute all relevant correlation functions exactly, in the purely bosonic, as well as in the supersymmetric case. However, it is not always clear what is the role of the cosmological constant in this gauge (see discussion in ). In the conformal gauge, many results were rederived in . In this Chapter we start with the purely bosonic case, which is well established.
2D-Gravity in Non-Critical Strings: Discrete and Continuum Approaches (Planetology) by Elcio Abdalla