315 research outputs found
Lefschetz thimble structure in one-dimensional lattice Thirring model at finite density
We investigate Lefschetz thimble structure of the complexified
path-integration in the one-dimensional lattice massive Thirring model with
finite chemical potential. The lattice model is formulated with staggered
fermions and a compact auxiliary vector boson (a link field), and the whole set
of the critical points (the complex saddle points) are sorted out, where each
critical point turns out to be in a one-to-one correspondence with a singular
point of the effective action (or a zero point of the fermion determinant). For
a subset of critical point solutions in the uniform-field subspace, we examine
the upward and downward cycles and the Stokes phenomenon with varying the
chemical potential, and we identify the intersection numbers to determine the
thimbles contributing to the path-integration of the partition function. We
show that the original integration path becomes equivalent to a single
Lefschetz thimble at small and large chemical potentials, while in the
crossover region multi thimbles must contribute to the path integration.
Finally, reducing the model to a uniform field space, we study the relative
importance of multiple thimble contributions and their behavior toward
continuum and low-temperature limits quantitatively, and see how the rapid
crossover behavior is recovered by adding the multi thimble contributions at
low temperatures. Those findings will be useful for performing Monte-Carlo
simulations on the Lefschetz thimbles.Comment: 32 pages, 14 figures (typo etc. corrected
Nontriviality of Gauge-Higgs-Yukawa System and Renormalizability of Gauged NJL Model
In the leading order of a modified 1/Nc expansion, we show that a class of
gauge-Higgs-Yukawa systems in four dimensions give non-trivial and well-defined
theories in the continuum limit. The renormalized Yukawa coupling y and the
quartic scalar coupling \lambda have to lie on a certain line in the
(y,\lambda) plane and the line terminates at an upper bound. The gauged
Nambu--Jona-Lasinio (NJL) model in the limit of its ultraviolet cutoff going to
infinity, is shown to become equivalent to the gauge-Higgs-Yukawa system with
the coupling constants just on that terminating point. This proves the
renormalizability of the gauged NJL model in four dimensions. The effective
potential for the gauged NJL model is calculated by using renormalization group
technique and confirmed to be consistent with the previous result by Kondo,
Tanabashi and Yamawaki obtained by the ladder Schwinger-Dyson equation.Comment: 32 pages, LaTeX, 3 Postscript Figures are included as uuencoded files
(need `epsf.tex'), KUNS-1278, HE(TH) 94/10 / NIIG-DP-94-2. (Several
corrections in the introduction and references.
Symmetry and Symmetry Restoration of Lattice Chiral Fermion in the Overlap Formalism
Three aspects of symmetry structure of lattice chiral fermion in the overlap
formalism are discussed. By the weak coupling expansion of the overlap Dirac
operator, the axial anomaly associated to the chiral transformation proposed by
Luescher is evaluated and is shown to have the correct form of the topological
charge density for perturbative backgrounds. Next we discuss the exponential
suppression of the self-energy correction of the lightest mode in the
domain-wall fermion/truncated overlap. Finally, we consider a supersymmetric
extension of the overlap formula in the case of the chiral multiplet and
examine the symmetry structure of the action.Comment: LATTICE98(chiral), 3 pages, LaTeX using espcrc2.st
Schroedinger functional formalism with domain-wall fermion
Finite volume renormalization scheme is one of the most fascinating scheme
for non-perturbative renormalization on lattice.
By using the step scaling function one can follow running of renormalized
quantities with reasonable cost.
It has been established the Schroedinger functional is very convenient to
define a field theory in a finite volume for the renormalization scheme.
The Schroedinger functional, which is characterized by a
Dirichlet boundary condition in temporal direction, is well defined and works
well for the Yang-Mills theory and QCD with the Wilson fermion.
However one easily runs into difficulties if one sets the same sort of the
Dirichlet boundary condition for the overlap Dirac operator or the domain-wall
fermion.
In this paper we propose an orbifolding projection procedure to impose the
Schroedinger functional Dirichlet boundary condition on the domain-wall
fermion.Comment: 32 page
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