Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Small Instantons in $CP^1$ and $CP^2$ Sigma Models   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.

17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga