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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...
Autores principales: | , , , |
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Lenguaje: | eng |
Publicado: |
1993
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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. |
id | cern-243683 |
institution | Organización Europea para la Investigación Nuclear |
language | eng |
publishDate | 1993 |
record_format | invenio |
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 |
work_keys_str_mv | AT browerrichardc symmetrybreakinginthedoublewellhermitianmatrixmodels AT deonivedita symmetrybreakinginthedoublewellhermitianmatrixmodels AT jainsanjay symmetrybreakinginthedoublewellhermitianmatrixmodels AT tanchungi symmetrybreakinginthedoublewellhermitianmatrixmodels |