11,985 research outputs found

### Large-N reduction of SU(N) Yang-Mills theory with massive adjoint overlap fermions

We study four dimensional large-N SU(N) Yang-Mills theory coupled to adjoint
overlap fermions on a single site lattice. Lattice simulations along with
perturbation theory show that the bare quark mass has to be taken to zero as
one takes the continuum limit in order to be in the physically relevant
center-symmetric phase. But, it seems that it is possible to take the continuum
limit with any renormalized quark mass and still be in the center-symmetric
physics. We have also conducted a study of the correlations between Polyakov
loop operators in different directions and obtained the range for the Wilson
mass parameter that enters the overlap Dirac operator.Comment: 8 pages, 5 figure

### Lacunary Fourier series and a qualitative uncertainty principle for compact Lie groups

We define lacunary Fourier series on a compact connected semisimple Lie group
$G$. If $f \in L^1(G)$ has lacunary Fourier series, and vanishes on a non empty
open set, then we prove that $f$ vanishes identically. This may be viewed as a
qualitative uncertainty principle

### Truncated Overlap Fermions

In this talk I propose a new computational scheme with overlap fermions and a
fast algorithm to invert the corresponding Dirac operator.Comment: LATTICE99(algorithms

### Two dimensional fermions in three dimensional YM

Dirac fermions in the fundamental representation of SU(N) live on the surface
of a cylinder embedded in $R^3$ and interact with a three dimensional SU(N)
Yang Mills vector potential preserving a global chiral symmetry at finite $N$.
As the circumference of the cylinder is varied from small to large, the chiral
symmetry gets spontaneously broken in the infinite $N$ limit at a typical bulk
scale. Replacing three dimensional YM by four dimensional YM introduces
non-trivial renormalization effects.Comment: 21 pages, 7 figures, 5 table

### Asymptotics of Harish-Chandra expansions, bounded hypergeometric functions associated with root systems, and applications

A series expansion for Heckman-Opdam hypergeometric functions
$\varphi_\lambda$ is obtained for all $\lambda \in \mathfrak a^*_{\mathbb C}.$
As a consequence, estimates for $\varphi_\lambda$ away from the walls of a Weyl
chamber are established. We also characterize the bounded hypergeometric
functions and thus prove an analogue of the celebrated theorem of Helgason and
Johnson on the bounded spherical functions on a Riemannian symmetric space of
the noncompact type. The $L^p$-theory for the hypergeometric Fourier transform
is developed for $0<p<2$. In particular, an inversion formula is proved when
$1\leq p <2$

### Chiral Symmetry Restoration in the Schwinger Model with Domain Wall Fermions

Domain Wall Fermions utilize an extra space time dimension to provide a
method for restoring the regularization induced chiral symmetry breaking in
lattice vector gauge theories even at finite lattice spacing. The breaking is
restored at an exponential rate as the size of the extra dimension increases.
Before this method can be used in dynamical simulations of lattice QCD, the
dependence of the restoration rate to the other parameters of the theory and,
in particular, the lattice spacing must be investigated. In this paper such an
investigation is carried out in the context of the two flavor lattice Schwinger
model.Comment: LaTeX, 37 pages including 18 figures. Added comments regarding power
law fitting in sect 7. Also, few changes were made to elucidate the content
in sect. 5.1 and 5.3. To appear in Phys. Rev.

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