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

ISBN-10: 3540483365

ISBN-13: 9783540483366

ISBN-10: 3540578056

ISBN-13: 9783540578055

This ebook encompasses a survey of using the Liouville (and super-Liouville) equation in (super)string concept outdoor the serious measurement, and of the complementary process according to the discretized space-time, often called the matrix version process. Supersymmetry is given specific realization, either within the continuum formula, through the Liouville equation, and during the respect of the super-eigenvalue challenge. The equipment offered listed here are vital in quite a few advanced difficulties, e.g. random surfaces, 2-D gravity and large-N quantum chromodynamics. The comparability of alternative tools within the examine of such difficulties allows a cross-evaluation of the consequences while either equipment are acceptable and new predictions while just one of the equipment can be used.

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**Extra info for 2D-Gravity in Non-Critical Strings: Discrete and Continuum Approaches**

**Example text**

First of all observe that in the limit of zero momenta (k J --t 0) we have f3 J --t a+ (and t(f3; - k;) --t -p) which means that the tachyonic operator reduces to the cosmological term for vanishing momentum. ( -p)]' factor in the amplitude A 3 as a multiple point correlator with some points having zero momentum. For further discussion we separate the cases c = 1 and c < 1. 105). L factor m the measure of the path integral. e. 67) to obtain a result which holds for c < 1. The case c = 1, or equivalently ao = 0 requires more care in redefining the vertices Tk and the cosmological constant JL.

Therefore, it is possible that string theory has a phase 27 transition at this point, where the string degenerates to a branched polymer or is in a crumpled phase 51 • Therefore at this point one is led to the study of random surfaces, and related critical phenomena52 . The propagation of strings along random surfaces is a rather general problem in physics. It describes low energy QCD 53 in the large N limit. In fact we may argue that the large N limit is related to two-dimensional gravity (Liouville theory)54.

92] each Or r' operator which appears in the correlation function should be integrated over the' t~o-dimensionalsurface and dressed by the Liouville field; this means that one is interested in correlation functions such as: where the matter and gravitational contributions are calculated separately. The dressing {3, is determined imposing that Or,r:e,8,4>(z,) be an operator with conformal dimension one. 21) where we have used the free field representation for the Liouville field in the presence of a constant background charge Q.

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

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