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

By Elcio Abdalla

This booklet incorporates a survey of using the Liouville (and super-Liouville) equation in (super)string idea open air the serious size, and of the complementary method in response to the discretized space-time, often called the matrix version method. Supersymmetry is given specific realization, either within the continuum formula, via the Liouville equation, and during the respect of the super-eigenvalue challenge. The equipment offered listed below are vital in lots 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 implications whilst either tools are acceptable and new predictions whilst just one of the equipment can be used.

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P,-nr(n) '" p" as a consequence of the aforementioned non universality (see also -In -Inp, [93]). The starting point is the result obtained in the matrix model approach for the partition function on a torus of radius R coupled to gravity by the authors of ref. 17) where X denotes the matter fields, and 7 is the moduli parameter which in the case of genus one is the two-dimensional region 7 = 71 +i72, 72 > 0, 17 I > 1, 71 < This result has been obtained again performing the integral over the moduli with a proper normalization in ref.

To calculate the amplitudes ratio in order to compare with the results obtained by Dotsenko (Eq. 85) Observe that we are analyzing the minimal model case where the momenta assume discrete values given by the Kac formula k, mentum conservation law we have n =~ = (l~r')d+ + (l~r:)d_. Using the mo- (2:;=1 r, - 1) and m = ~ (2:;=1 r: - 1), where ii, and iii are obtained from nand m when r3 = r; = 1. 50) for the dressing ,8, we obtain exactly Dotsenko's result 77 , which agrees with those oftop Eq. 45).

The calculation of the O-point (partition) function for the interacting theory (p. + )-point function in the free theory. + = n. + are functions of c we are led to some "magic" values given by c = 6n2t:~i\-n) At this point of the computation, the zero mode Integration seems to be a useless technique. Indeed, in spite of the fact that we expect a calculable result for c assuming the above values, one has singularities of the type r( -n). For this reason, in ref. [72] a more conservative attitude has been adopted, and only fixed area correlators have been computed.

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