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Symmetry breaking in the double-well hermitian matrix models

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 coefficie...

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Autores principales: Brower, Richard C., Deo, Nivedita, Jain, Sanjay, Tan, Chung-I
Lenguaje:eng
Publicado: 1993
Materias:
Acceso en línea:https://dx.doi.org/10.1016/0550-3213(93)90430-W
http://cds.cern.ch/record/243683
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author Brower, Richard C.
Deo, Nivedita
Jain, Sanjay
Tan, Chung-I
author_facet Brower, Richard C.
Deo, Nivedita
Jain, Sanjay
Tan, Chung-I
author_sort Brower, Richard C.
collection CERN
description 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.
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institution Organización Europea para la Investigación Nuclear
language eng
publishDate 1993
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spelling cern-2436832023-03-14T17:13:10Zdoi:10.1016/0550-3213(93)90430-Whttp://cds.cern.ch/record/243683engBrower, Richard C.Deo, NiveditaJain, SanjayTan, Chung-ISymmetry breaking in the double-well hermitian matrix modelsParticle Physics - TheoryWe 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.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.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.We study symmetry breaking in Z 2 symmetric large N matrix models. In the planar approximation for both the symmetric double-well φ 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 θ ( x ), for each value of x = n / N <1. In the duoble scaling limit, this class reduces to a smaller family of solutions with distinct free energies already at the torus level. For the double-well φ 4 theory the double scaling string equations are parameterized by a conserved angular momentum parameter in the range 0 ⩽ l < ∞ and a single arbitrary U(1) phase angle.hep-th/9212127HUTP-92-A035BROWN-HET-863CERN-TH-6611-92LPTHE-92-29BROWN-HET-863CERN-TH-6611-92HUTP-92-A-035LPTHE-92-29oai:cds.cern.ch:2436831993
spellingShingle Particle Physics - Theory
Brower, Richard C.
Deo, Nivedita
Jain, Sanjay
Tan, Chung-I
Symmetry breaking in the double-well hermitian matrix models
title Symmetry breaking in the double-well hermitian matrix models
title_full Symmetry breaking in the double-well hermitian matrix models
title_fullStr Symmetry breaking in the double-well hermitian matrix models
title_full_unstemmed Symmetry breaking in the double-well hermitian matrix models
title_short Symmetry breaking in the double-well hermitian matrix models
title_sort symmetry breaking in the double-well hermitian matrix models
topic Particle Physics - Theory
url https://dx.doi.org/10.1016/0550-3213(93)90430-W
http://cds.cern.ch/record/243683
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AT deonivedita symmetrybreakinginthedoublewellhermitianmatrixmodels
AT jainsanjay symmetrybreakinginthedoublewellhermitianmatrixmodels
AT tanchungi symmetrybreakinginthedoublewellhermitianmatrixmodels