dorsal/arxiv
View SchemaThe Spectral Density of the Dirac Operator above T_c
| Authors | Thomas D. Cohen |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/9801061 |
| URL | https://arxiv.org/abs/nucl-th/9801061 |
Abstract
The importance of the spectral density of the Dirac operator in studying spontaneous chiral symmetry breaking and anomalous U(1) axial symmetry breaking are reviewed. It is shown that both types of symmetry breaking can be traced to effects of modes near zero virtuality. Above T_c, where chiral symmetry is restored, it is shown on general grounds that (in the massless quark limit), the density of states vanishes at zero virtuality faster than $\lambda$, where $\lambda$ is the virtuality-- $\rho(\lambda) \sim |\lambda|^\alpha$ is not possible for $\alpha \le 1$. Isospin invariance is used to show that $\rho(\lambda) \sim m_q^{1-\alpha} |\lambda|^\alpha$ is also not possible for $\alpha \le 1$. State-of-the-art lattice calculations are reviewed in light of these constraints. In particular, it is argued that violations of these constraints by lattice calculations indicate possible large systematic errors; this raises questions about $U(1)_A$ violating effects seen on the lattice.It is also shown that above $T_c$, the Dirac spectrum has a gap near zero (in the $m_q \to 0$ limit) unless contributions from quark-line-connected and disconnected contributions conspire to cancel.
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"abstract": "The importance of the spectral density of the Dirac operator in studying\nspontaneous chiral symmetry breaking and anomalous U(1) axial symmetry breaking\nare reviewed. It is shown that both types of symmetry breaking can be traced to\neffects of modes near zero virtuality. Above T_c, where chiral symmetry is\nrestored, it is shown on general grounds that (in the massless quark limit),\nthe density of states vanishes at zero virtuality faster than $\\lambda$, where\n$\\lambda$ is the virtuality-- $\\rho(\\lambda) \\sim |\\lambda|^\\alpha$ is not\npossible for $\\alpha \\le 1$. Isospin invariance is used to show that\n$\\rho(\\lambda) \\sim m_q^{1-\\alpha} |\\lambda|^\\alpha$ is also not possible for\n$\\alpha \\le 1$. State-of-the-art lattice calculations are reviewed in light of\nthese constraints. In particular, it is argued that violations of these\nconstraints by lattice calculations indicate possible large systematic errors;\nthis raises questions about $U(1)_A$ violating effects seen on the lattice.It\nis also shown that above $T_c$, the Dirac spectrum has a gap near zero (in the\n$m_q \\to 0$ limit) unless contributions from quark-line-connected and\ndisconnected contributions conspire to cancel.",
"arxiv_id": "nucl-th/9801061",
"authors": [
"Thomas D. Cohen"
],
"categories": [
"nucl-th"
],
"title": "The Spectral Density of the Dirac Operator above T_c",
"url": "https://arxiv.org/abs/nucl-th/9801061"
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