Small Instantons in $CP^1$ and $CP^2$ Sigma Models

Details Small Instantons in $CP^1$ and $CP^2$ Sigma Models Small Instantons in $CP^1$ and $CP^2$ Sigma Models

2006-07-20

arxiv.org/abs/hep-lat/0607026v1

Phys.Rev.D75:065031,2007

Physics

High Energy Physics

High Energy Physics - Lattice

33 pages, 12 figures

Scientific paper

10.1103/PhysRevD.75.065031

The anomalous scaling behavior of the topological susceptibility $\chi_t$ 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 $\chi_t$ 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 L\"{u}scher'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.

Affiliated with

Also associated with

No associations

Rating

Small Instantons in $CP^1$ and $CP^2$ Sigma Models does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Small Instantons in $CP^1$ and $CP^2$ Sigma Models, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Small Instantons in $CP^1$ and $CP^2$ Sigma Models will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-79013