New critical behavior in d = 0 large-N matrix models

Das, Sumit R. ; Dhar, Avinash ; Sengupta, Anirvan M. ; Wadia, Spenta R. (1990) New critical behavior in d = 0 large-N matrix models Modern Physics Letters A, 5 (13). pp. 1041-1056. ISSN 0217-7323

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The non-perturbative formulation of 2-dimensional quantum gravity in terms of the large-N limit of matrix models is studied to include the effects of higher order curvature terms. This leads to matrix models whose potential contains a symmetry breaking term of the form Tr φAφA, where A is a given fixed matrix. This is studied in d = 0 dimensions and effectively induces additional terms of the form (Tr φk)2 in the one matrix potential. An exact solution to leading order of the potential V(φ) = 1/2 Tr φ2 + g/N Tr φ4 + g'/N2 (Tr φ2)2 is presented leading to 3 phases: γ = -1/2 (smooth surfaces), γ = 1/2 (branched polymer) and γ = 1/3 (intermediate phase). Including a Tr φ6 term in the potential gives rise to an additional phase with γ = 1/4. It is conjectured that for the general polynomial potential there are phases with γ = 1/n, n = 2, 3, .... The γ > 0 phases may correspond to c > 1 matter coupled to 2-dimensional gravity.

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Deposited On:28 Oct 2010 11:03
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