2D-Gravity in Non-Critical Strings: Discrete and Continuum - download pdf or read online

By Elcio Abdalla

ISBN-10: 3540578056

ISBN-13: 9783540578055

This booklet incorporates a survey of using the Liouville (and super-Liouville) equation in (super)string concept outdoors the serious size, and of the complementary technique in response to the discretized space-time, often called the matrix version procedure. Supersymmetry is given specific consciousness, either within the continuum formula, by way of the Liouville equation, and during the dignity of the super-eigenvalue challenge. The equipment awarded listed below are very important in quite a few advanced difficulties, e.g. random surfaces, 2-D gravity and large-N quantum chromodynamics. The comparability of other tools within the research of such difficulties allows a cross-evaluation of the consequences while either equipment are appropriate and new predictions whilst just one of the tools can be used.

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Because of its classical origin, those singularities could be detected in a semiclassical21 analysis. 15) The universality of the finite piece suggests that the implicit singularity in the factor JLnr( -n) be disregarded such that only the finite piece has physical content. As we shall see in the next section with this interpretation we shall be able to deal with the quantum Liouville theory. 2. The 3-Point Function Before describing the zero mode technique in more detail, it is important to say some words about the results of Bershadsky and Klebanov 92 who have calculated the partition function on the torus in the case of a boson compactified into a circle of radius R coupled to two-dimensional gravity via Liouville theory.

In the matter sector 79 ,80. The total action is the same as in the previous section (S L + skt). '\~n. ,\~ f( -8) IT f d 2z, IT f d 2t) IT f d2rk m. 89) (Q p,). =1 )=4 n N II It. <) m x II 2P ,<)=1 n X :, s 2 ,=1 X 4P Iz, - z) 1 ,<)=4 s X II ,<)=1 m Ir. 76), we have also a) = k 1 k) - PIP), ii) = d+k) , p) = k 2k) -P2P)l jj) = d_k)l p;) = t(klk) - PIP)), p) = -a+p)l with 4 :::; j,l :::; N. 91) is very difficult to be calculated in general (even in the case n = m = 0). However we notice that it possesses a set 49 of symmetries: It is invariant under X, --+ 1 - X, once we exchange variabl(~s as a +-t f3 , a~ +-t f3; , a +-t jj and a' +-t jj'.

M x II 2P ,<)=1 n X :, s 2 ,=1 X 4P Iz, - z) 1 ,<)=4 s X II ,<)=1 m Ir. 76), we have also a) = k 1 k) - PIP), ii) = d+k) , p) = k 2k) -P2P)l jj) = d_k)l p;) = t(klk) - PIP)), p) = -a+p)l with 4 :::; j,l :::; N. 91) is very difficult to be calculated in general (even in the case n = m = 0). However we notice that it possesses a set 49 of symmetries: It is invariant under X, --+ 1 - X, once we exchange variabl(~s as a +-t f3 , a~ +-t f3; , a +-t jj and a' +-t jj'. , is guaranteed if x. 92) jj' - p(m - 1) + 2n N 2 - a'0 - f3'0 - 2 LJ) " p't - naJ - ma') 1=4 (,<1) The above symmetries still do not permit to calculate Fir.

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


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