Small Instantons in $CP^1$ and $CP^2$ Sigma Models
| dc.creator | Lian, Yaogang | |
| dc.creator | Thacker, H. B. | |
| dc.date | 2006-07-20 | |
| dc.date.accessioned | 2026-07-07T10:24:45Z | |
| dc.date.available | 2026-07-07T10:24:45Z | |
| dc.description | The anomalous scaling behavior of the topological susceptibility $χ_t$ in two-dimensional $CP^{N-1}$ sigma models for $N\leq 3$ is studied using the overlap Dirac operator construction of the lattice topological charge density. The divergence of $χ_t$ in these models is traced to the presence of small instantons with a radius of order $a$ (= lattice spacing), which are directly observed on the lattice. The observation of these small instantons provides detailed confirmation of Lüscher's argument that such short-distance excitations, with quantized topological charge, should be the dominant topological fluctuations in $CP^1$ and $CP^2$, leading to a divergent topological susceptibility in the continuum limit. For the $\CP$ models with $N>3$ the topological susceptibility is observed to scale properly with the mass gap. These larger $N$ models are not dominated by instantons, but rather by coherent, one-dimensional regions of topological charge which can be interpreted as domain wall or Wilson line excitations and are analogous to D-brane or ``Wilson bag'' excitations in QCD. In Lorentz gauge, the small instantons and Wilson line excitations can be described, respectively, in terms of poles and cuts of an analytic gauge potential. | |
| dc.description | 33 pages, 12 figures | |
| dc.identifier | https://arxiv.org/abs/hep-lat/0607026 | |
| dc.identifier | http://arxiv.org/abs/hep-lat/0607026 | |
| dc.identifier | Phys.Rev.D75:065031,2007 | |
| dc.identifier | doi:10.1103/PhysRevD.75.065031 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/176297 | |
| dc.subject | High Energy Physics - Lattice | |
| dc.title | Small Instantons in $CP^1$ and $CP^2$ Sigma Models | |
| dc.type | text |