12 research outputs found
The staggered domain wall fermion method
A different lattice fermion method is introduced. Staggered domain wall
fermions are defined in 2n+1 dimensions and describe 2^n flavors of light
lattice fermions with exact U(1) x U(1) chiral symmetry in 2n dimensions. As
the size of the extra dimension becomes large, 2^n chiral flavors with the same
chiral charge are expected to be localized on each boundary and the full
SU(2^n) x SU(2^n) flavor chiral symmetry is expected to be recovered. SDWF give
a different perspective into the inherent flavor mixing of lattice fermions and
by design present an advantage for numerical simulations of lattice QCD
thermodynamics. The chiral and topological index properties of the SDWF Dirac
operator are investigated. And, there is a surprise ending...Comment: revtex4, 7 figures, minor revisions, 2 references adde
Fermion-scalar interactions with domain wall fermions
Domain wall fermions are defined on a lattice with an extra direction the
size of which controls the chiral properties of the theory. When gauge fields
are coupled to domain wall fermions the extra direction is treated as an
internal flavor space. Here it is found that this is not the case for scalar
fields. Instead, the interaction takes place only along the link that connects
the boundaries of the extra direction. This reveals a richness in the way
different spin particles are coupled to domain wall fermions. As an
application, 4-Fermi models are studied using large N techniques and the
results are supported by numerical simulations with N=2. It is found that the
chiral properties of domain wall fermions in these models are good across a
large range of couplings and that a phase with parity-flavor broken symmetry
can develop for negative bare masses if the number of sites along the extra
direction is finite.Comment: LaTeX, 17 pages, 8 eps figures; comment regarding the width of Aoki
phase added in sec. 3; references adde
Solving the local cohomology problem in U(1) chiral gauge theories within a finite lattice
In the gauge-invariant construction of abelian chiral gauge theories on the
lattice based on the Ginsparg-Wilson relation, the gauge anomaly is topological
and its cohomologically trivial part plays the role of the local counter term.
We give a prescription to solve the local cohomology problem within a finite
lattice by reformulating the Poincar\'e lemma so that it holds true on the
finite lattice up to exponentially small corrections. We then argue that the
path-integral measure of Weyl fermions can be constructed directly from the
quantities defined on the finite lattice.Comment: revised version, 35pages, using JHEP3.cl
The effects of an extra U(1) axial condensate on the radiative decay eta' --> gamma gamma at finite temperature
Supported by recent lattice results, we consider a scenario in which a
U(1)-breaking condensate survives across the chiral transition in QCD. This
scenario has important consequences on the pseudoscalar-meson sector, which can
be studied using an effective Lagrangian model. In particular, generalizing the
results obtained in a previous paper (where the zero-temperature case was
considered), we study the effects of this U(1) chiral condensate on the
radiative decay eta' --> gamma gamma at finite temperature.Comment: 15 pages, LaTeX fil
The finite-temperature chiral transition in QCD with adjoint fermions
We study the nature of the finite-temperature chiral transition in QCD with
N_f light quarks in the adjoint representation (aQCD). Renormalization-group
arguments show that the transition can be continuous if a stable fixed point
exists in the renormalization-group flow of the corresponding three-dimensional
Phi^4 theory with a complex 2N_f x 2N_f symmetric matrix field and
symmetry-breaking pattern SU(2N_f)->SO(2N_f). This issue is investigated by
exploiting two three-dimensional perturbative approaches, the massless
minimal-subtraction scheme without epsilon expansion and a massive scheme in
which correlation functions are renormalized at zero momentum. We compute the
renormalization-group functions in the two schemes to five and six loops
respectively, and determine their large-order behavior.
The analyses of the series show the presence of a stable three-dimensional
fixed point characterized by the symmetry-breaking pattern SU(4)->SO(4). This
fixed point does not appear in an epsilon-expansion analysis and therefore does
not exist close to four dimensions. The finite-temperature chiral transition in
two-flavor aQCD can therefore be continuous; in this case its critical behavior
is determined by this new SU(4)/SO(4) universality class. One-flavor aQCD may
show a more complex phase diagram with two phase transitions. One of them, if
continuous, should belong to the O(3) vector universality class.Comment: 36 page
Lattice Study of the Massive Schwinger Model with a term under L\"uscher's "Admissibility" condition
We present a numerical study of the massive two-flavor QED in two dimensions
with the gauge action proposed by L\"uscher, which allows only ``admissible''
gauge fields. We find that the admissibility condition does not allow any
topology changes by the local updation in Hybrid Monte Carlo algorithm so that
the configurations in each topological sector can be generated separately. By
developing a new method to sum over different topological sectors, we
investigate vacuum effects. Combining with domain-wall fermion action,
we obtain the fermion mass dependence and dependence of the meson
masses, which are consistent with the analytic results by mass perturbation in
the continuum theory.Comment: 3 pages, Lattice2003(chiral
Effective Lagrangian for strongly coupled domain wall fermions
We derive the effective Lagrangian for mesons in lattice gauge theory with
domain-wall fermions in the strong-coupling and large-N_c limits. We use the
formalism of supergroups to deal with the Pauli-Villars fields, needed to
regulate the contributions of the heavy fermions. We calculate the spectrum of
pseudo-Goldstone bosons and show that domain wall fermions are doubled and
massive in this regime. Since we take the extent and lattice spacing of the
fifth dimension to infinity and zero respectively, our conclusions apply also
to overlap fermions.Comment: 26 pp. RevTeX and 3 figures; corrected error in symmetry breaking
scheme and added comments to discussio
Large N_c, chiral approach to M_eta' at finite temperature
We study the temperature dependence of the eta and eta' meson masses within
the framework of U(3)_L x U(3)_R chiral perturbation theory, up to
next-to-leading order in a simultaneous expansion in momenta, quark masses and
number of colours. We find that both masses decrease at low temperatures, but
only very slightly. We analyze higher order corrections and argue that large
N_c suggests a discontinuous drop of M_eta' at the critical temperature of
deconfinement T_c, consistent with a first order transition to a phase with
approximate U(1)_A symmetry.Comment: 21 pages, 6 figures. 2 footnotes added, 1 reference changed and 1
typo corrected. To be published in Phys. Rev.
On the nature of the finite-temperature transition in QCD
We discuss the nature of the finite-temperature transition in QCD with N_f
massless flavors. Universality arguments show that a continuous (second-order)
transition must be related to a 3-D universality class characterized by a
complex N_f X N_f matrix order parameter and by the symmetry-breaking pattern
[SU(N_f)_L X SU(N_f)_R]/Z(N_f)_V -> SU(N_f)_V/Z(N_f)_V, or [U(N_f)_L X
U(N_f)_R]/U(1)_V -> U(N_f)_V/U(1)_V if the U(1)_A symmetry is effectively
restored at T_c. The existence of any of these universality classes requires
the presence of a stable fixed point in the corresponding 3-D Phi^4 theory with
the expected symmetry-breaking pattern. Otherwise, the transition is of first
order. In order to search for stable fixed points in these Phi^4 theories, we
exploit a 3-D perturbative approach in which physical quantities are expanded
in powers of appropriate renormalized quartic couplings. We compute the
corresponding Callan-Symanzik beta-functions to six loops. We also determine
the large-order behavior to further constrain the analysis. No stable fixed
point is found, except for N_f=2, corresponding to the symmetry-breaking
pattern [SU(2)_L X SU(2)_R]/Z(2)_V -> SU(2)_V/Z(2)_V equivalent to O(4) ->
O(3). Our results confirm and put on a firmer ground earlier analyses performed
close to four dimensions, based on first-order calculations in the framework of
the epsilon=4-d expansion. These results indicate that the finite-temperature
phase transition in QCD is of first order for N_f>2. A continuous transition is
allowed only for N_f=2. But, since the theory with symmetry-breaking pattern
[U(2)_L X U(2)_R]/U(1)_V -> U(2)_V/U(1)_V does not have stable fixed points,
the transition can be continuous only if the effective breaking of the U(1)_A
symmetry is sufficiently large.Comment: 30 pages, 3 figs, minor correction