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Report number	hep-th/9212127 ; HUTP-92-A035 ; BROWN-HET-863 ; CERN-TH-6611-92 ; LPTHE-92-29 ; BROWN-HET-863 ; CERN-TH-6611-92 ; HUTP-92-A-035 ; LPTHE-92-29
Title	Symmetry breaking in the double-well hermitian matrix models
Author(s)	Brower, Richard C. (Boston U. ; CERN) ; Deo, Nivedita (Harvard U.) ; Jain, Sanjay (Harvard U.) ; Tan, Chung-I (Brown U.)
Affiliation	(Boston Univ.) ; (CERN) ; (Harvard Univ. Cambridge)
Publication	1993
Imprint	Aug 1992
Number of pages	24
In:	Nucl. Phys. B 405 (1993) 166-187
DOI	10.1016/0550-3213(93)90430-W
Subject category	Particle Physics - Theory
Abstract	We study symmetry breaking in $Z_2$ symmetric large $N$ matrix models. In the planar approximation for both the symmetric double-well $\phi 4$ model and the symmetric Penner model, we find there is an infinite family of broken symmetry solutions characterized by different sets of recursion coefficients $R_n$ and $S_n$ that all lead to identical free energies and eigenvalue densities. These solutions can be parameterized by an arbitrary angle $\theta(x)$, for each value of $x = n/N < 1$. In the double scaling limit, this class reduces to a smaller family of solutions with distinct free energies already at the torus level. For the double-well $\phi 4$ theory the double scaling string equations are parameterized by a conserved angular momentum parameter in the range $0 \le l < \infty$ and a single arbitrary $U(1)$ phase angle.
Copyright/License	Copyright @ unknown. Published by Elsevier B.V.

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Email contact: [email protected] (Richard Brower)