By Elcio Abdalla

ISBN-10: 3540578056

ISBN-13: 9783540578055

This publication incorporates a survey of using the Liouville (and super-Liouville) equation in (super)string conception open air the serious measurement, and of the complementary procedure in keeping with the discretized space-time, referred to as the matrix version method. Supersymmetry is given specific recognition, either within the continuum formula, by way of the Liouville equation, and during the dignity of the super-eigenvalue challenge. The tools awarded listed below are vital in a good number of complicated difficulties, e.g. random surfaces, 2-D gravity and large-N quantum chromodynamics. The comparability of alternative equipment within the examine of such difficulties allows a cross-evaluation of the implications whilst either tools are appropriate and new predictions while just one of the tools can be utilized.

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

**Example text**

The first is that the Liouville field can be seen from the space-time point of view as an Euclidean time: ikX + (3 = i(p . f) with Pp. = ({3, k) and fp. 52) defining a massless particle for the tachyonic case. Therefore, we should define the energy as E = (3 +~, and the momentum as p = k - ao. l ) The above interpretation is equivalent to saying that the total action S corresponds to a string embedded in a two dimensional Euclidean space with a non-trivial background. We shall see (a posteriori) that the scattering amplitudes do confirm this interpretation.

In this case, the two critical points coincide at the spectrum is not of the rich type above. c= 1, and The extremely rich structure of the results thus obtained permits us to draw several new conclusions, and provides a clean method of computation which can be used to check the matrix model results as well as to extend them. The highly non-trivial comparison provides a valuable guide towards an understanding of the non-critical dynamics of strings and superstrings. 1. e. at genus-zero Riemann surfaces.

We have for the five point function, the following elements: for the first diagram in Fig. 121) hold in any kinematic region and do not need to be further examined in order to be extended. The last step now is to calculate the irreducible part A~PI. We first notice that the cuts at k, + kJ = 00 only appear due to zero energy intermediate particles (remember p = ±ilk, + k J - 001 = -iE), thus they can only correspond to the massless "tachyons" Tk. The remaining massive intermediate states only appear at (non-vanishing) discrete values of the momentum.

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

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