Nonperturbative effects in matrix models and vacua of two-dimensional gravity
Dec, 199215 pages
Published in:
- Phys.Lett.B 302 (1993) 403-410
e-Print:
- hep-th/9212106 [hep-th]
Report number:
- SACLAY-SPH-T-92-159
View in:
Citations per year
Abstract:
The most general large N eigenvalues distribution for the one matrix model is shown to consist of tree-like structures in the complex plane. For the m=2 critical point, such a split solution describes the strong coupling phase of 2d quantum gravity (c=0 non-critical string). It is obtained by taking combinations of complex contours in the matrix integral, and the relative weight of the contours is identified with the non-perturbative theta-parameter that fixes uniquely the solution of the string equation (Painleve I). This allows to recover by instanton methods results on the non-perturbative effects obtained by the Isomonodromic Deformation Method, and to construct for each theta-vacuum the observables (the loop correlation functions) which satisfy the loop equations. The breakdown of analyticity of the large N solution is related to the existence of poles for the loop operators.- quantum gravity
- dimension: 2
- matrix model
- vacuum state: Theta parameter
- partition function
- effect: nonperturbative
- effective potential
- critical phenomena
- field equations: solution
- analytic properties
References(25)
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- [1]
- [2]
- [3]
- [4]
- [5]
- [6]
- [7]
- [8]
- [9]
- [10]
- [11]
- [12]
- [13]
- [14]
- [15]
- [16]
- [17]
- [18]
- [19]
- [20]
- [21]
- [21]
- [22]
- [22]
- [23]