By Elcio Abdalla
This e-book encompasses a survey of using the Liouville (and super-Liouville) equation in (super)string idea open air the severe measurement, and of the complementary technique in accordance with the discretized space-time, referred to as the matrix version technique. 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 here are vital in a good number of advanced difficulties, e.g. random surfaces, 2-D gravity and large-N quantum chromodynamics. The comparability of other tools 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)
P,-nr(n) '" p" as a consequence of the aforementioned non universality (see also -In -Inp, ). 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.
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. ;2¢>. s. ;2¢>, which is presumably the correct cosmological term for the c = 1 case. 63). A more elegant way of understanding the cosmological term in the c = 1 theory, is by inspection using the space-time interpretation of the theory.
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).
2D-Gravity in Non-Critical Strings: Discrete and Continuum Approaches (Planetology) by Elcio Abdalla