2D-Gravity in Non-Critical Strings: Discrete and Continuum by E. Abdalla, M.C.B. Abdalla, D. Dalmazi, A. Zadra

By E. Abdalla, M.C.B. Abdalla, D. Dalmazi, A. Zadra

This publication incorporates a survey of using the Liouville (and super-Liouville) equation in (super)string thought outdoor the severe size, and of the complementary technique in keeping with the discretized space-time, often called the matrix version technique. Supersymmetry is given specific awareness, either within the continuum formula, through the Liouville equation, and during the respect of the super-eigenvalue challenge. The equipment provided listed here are vital in a number of complicated 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 tools are acceptable and new predictions while just one of the equipment can be used.

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Let us turn to the issues of the operator product expansion (OPE) and quantum solution. There is a well known anomaly in the quantum theory of twodimensional supergravity, generalizing the reparametrization anomaly. 132). 137) We will come back to this later on. The anomaly may be used to derive the short distance expansion of the fields. Starting from the correlator (9++(Zt}9++(Z2)'" 9++(Zn}rP+(yt}··· -rP+(Ym») J = "D9++"D-rP+9++(Zt}9++(Z2)'" 9++ (zn)-rP+ (yt) ... 133); as a consequence, we have a variation of the action given by the anomaly, Eq.

In the present case we can eliminate most of the parameters of f/r as a function of the independent variables a, f3, p, s and p) (for 4 ::; j ::; N - 1). i"-1 p) and we assume again ao < 0 in the region k 1 ,k2 ,·· ,k N ao, k N < ao. With this condition, Eqs. 97) where f'N lIl is still to be determined. 96), which can be checked using the formula ~(x + B) rv x 2B - 1 f(x)jf(-x) valid in the limit x ---+ 00. 99a) or A nm _ N - ( N 3 8 - -S+N-3) 8jlN-3P, [~(_P)]S X [L~(p-1)]m [A+~(p)r II ~ (~(I~; -k;)) .

130). 132b) where f+ is a parameter labelling the diffeomorphisms. 134c) (~). 134a) may be obtained truncating two dimensional supergravity with a matter multiplet 48 ,49. Let us turn to the issues of the operator product expansion (OPE) and quantum solution. There is a well known anomaly in the quantum theory of twodimensional supergravity, generalizing the reparametrization anomaly. 132). 137) We will come back to this later on. The anomaly may be used to derive the short distance expansion of the fields.

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