9,821 research outputs found
Improved actions and asymptotic scaling in lattice Yang-Mills theory
Improved actions in SU(2) and SU(3) lattice gauge theories are investigated
with an emphasis on asymptotic scaling. A new scheme for tadpole improvement is
proposed. The standard but heuristic tadpole improvement emerges from a mean
field approximation from the new approach. Scaling is investigated by means of
the large distance static quark potential. Both, the generic and the new
tadpole scheme yield significant improvements on asymptotic scaling when
compared with loop improved actions. A study of the rotational symmetry
breaking terms, however, reveals that only the new improvement scheme
efficiently eliminates the leading irrelevant term from the action.Comment: minor modifications, improved presentatio
Instantons, Fluxons and Open Gauge String Theory
We use the exact instanton expansion to illustrate various string
characteristics of noncommutative gauge theory in two dimensions. We analyse
the spectrum of the model and present some evidence in favour of Hagedorn and
fractal behaviours. The decompactification limit of noncommutative torus
instantons is shown to map in a very precise way, at both the classical and
quantum level, onto fluxon solutions on the noncommutative plane. The
weak-coupling singularities of the usual Gross-Taylor string partition function
for QCD on the torus are studied in the instanton representation and its double
scaling limit, appropriate for the mapping onto noncommutative gauge theory, is
shown to be a generating function for the volumes of the principal moduli
spaces of holomorphic differentials. The noncommutative deformation of this
moduli space geometry is described and appropriate open string interpretations
are proposed in terms of the fluxon expansion.Comment: 70 pages, 6 figure
Noncompact sigma-models: Large N expansion and thermodynamic limit
Noncompact SO(1,N) sigma-models are studied in terms of their large N
expansion in a lattice formulation in dimensions d \geq 2. Explicit results for
the spin and current two-point functions as well as for the Binder cumulant are
presented to next to leading order on a finite lattice. The dynamically
generated gap is negative and serves as a coupling-dependent infrared regulator
which vanishes in the limit of infinite lattice size. The cancellation of
infrared divergences in invariant correlation functions in this limit is
nontrivial and is in d=2 demonstrated by explicit computation for the above
quantities. For the Binder cumulant the thermodynamic limit is finite and is
given by 2/(N+1) in the order considered. Monte Carlo simulations suggest that
the remainder is small or zero. The potential implications for ``criticality''
and ``triviality'' of the theories in the SO(1,N) invariant sector are
discussed.Comment: 46 pages, 2 figure
Branching Asymptotics on Manifolds with Edge
We study pseudo-differential operators on a wedge with continuous and
variable discrete branching asymptotics.Comment: 54 pages, 1 figure
Bergman kernels and symplectic reduction
We generalize several recent results concerning the asymptotic expansions of
Bergman kernels to the framework of geometric quantization and establish an
asymptotic symplectic identification property. More precisely, we study the
asymptotic expansion of the -invariant Bergman kernel of the spin^c Dirac
operator associated with high tensor powers of a positive line bundle on a
symplectic manifold. We also develop a way to compute the coefficients of the
expansion, and compute the first few of them, especially, we obtain the scalar
curvature of the reduction space from the -invariant Bergman kernel on the
total space. These results generalize the corresponding results in the
non-equivariant setting, which has played a crucial role in the recent work of
Donaldson on stability of projective manifolds, to the geometric quantization
setting. As another kind of application, we generalize some Toeplitz operator
type properties in semi-classical analysis to the framework of geometric
quantization. The method we use is inspired by Local Index Theory, especially
by the analytic localization techniques developed by Bismut and Lebeau.Comment: 132 page
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