79 research outputs found
Large-N spacetime reduction and the sign and silver-blaze problems of dense QCD
We study the spacetime-reduced (Eguchi-Kawai) version of large-N QCD with
nonzero chemical potential. We explore a method to suppress the sign
fluctuations of the Dirac determinant in the hadronic phase; the method employs
a re-summation of gauge configurations that are related to each other by center
transformations. We numerically test this method in two dimensions, and find
that it successfully solves the silver-blaze problem. We analyze the system
further, and measure its free energy F, the average phase theta of its Dirac
determinant, and its chiral condensate . We show that F and
are independent of mu in the hadronic phase but that, as chiral
perturbation theory predicts, the quenched chiral condensate drops from its
mu=0 value when mu~(pion mass)/2. Finally, we find that the distribution of
theta qualitatively agrees with further, more recent, predictions from chiral
perturbation theory.Comment: 43 pages, 17 figure
Comments on large-N volume independence
We study aspects of the large-N volume independence on R**3 x L**G, where
L**G is a G-site lattice for Yang-Mills theory with adjoint Wilson-fermions. We
find the critical number of lattice sites above which the center-symmetry
analysis on L**G agrees with the one on the continuum S**1. For Wilson
parameter set to one and G>=2, the two analyses agree. One-loop radiative
corrections to Wilson-line masses are finite, reminiscent of the
UV-insensitivity of the Higgs mass in deconstruction/Little-Higgs theories.
Even for theories with G=1, volume independence in QCD(adj) may be guaranteed
to work by tuning one low-energy effective field theory parameter. Within the
parameter space of the theory, at most three operators of the 3d effective
field theory exhibit one-loop UV-sensitivity. This opens the analytical
prospect to study 4d non-perturbative physics by using lower dimensional field
theories (d=3, in our example).Comment: 12 pages; added small clarifications, published versio
Volume dependence of two-dimensional large-N QCD with a nonzero density of baryons
We take a first step towards the solution of QCD in 1+1 dimensions at nonzero
density. We regularize the theory in the UV by using a lattice and in the IR by
putting the theory in a box of spatial size L. After fixing to axial gauge we
use the coherent states approach to obtain the large-N classical Hamiltonian H
that describes color neutral quark-antiquark pairs interacting with spatial
Polyakov loops in the background of baryons. Minimizing H we get a regularized
form of the `t Hooft equation that depends on the expectation values of the
Polyakov loops. Analyzing the L-dependence of this equation we show how volume
independence, a la Eguchi and Kawai, emerges in the large-N limit, and how it
depends on the expectation values of the Polyakov loops. We describe how this
independence relies on the realization of translation symmetry, in particular
when the ground state contains a baryon crystal. Finally, we remark on the
implications of our results on studying baryon density in large-N QCD within
single-site lattice theories, and on some general lessons concerning the way
four-dimensional large-N QCD behaves in the presence of baryons.Comment: 32 pages, 3 figures. New version much more reader friendly and also
emphasizes the exact nature of the approac
First study of the gluon-quark-antiquark static potential in SU(3) Lattice QCD
We study the long distance interaction for hybrid hadrons, with a static
gluon, a quark and an antiquark with lattice QCD techniques. A Wilson loop
adequate to the static hybrid three-body system is developed and, using a 24^3
x 48 periodic lattice with beta=6.2 and a ~ 0.075 fm, two different geometries
for the gluon-quark segment and the gluon-antiquark segment are investigated.
When these segments are perpendicular, the static potential is compatible with
confinement realized with a pair of fundamental strings, one linking the gluon
to the quark and another linking the same gluon to the antiquark. When the
segments are parallel and superposed, the total string tension is larger and
agrees with the Casimir Scaling measured by Bali. This can be interpreted with
a type-II superconductor analogy for the confinement in QCD, with repulsion of
the fundamental strings and with the string tension of the first topological
excitation of the string (the adjoint string) larger than the double of the
fundamental string tension.Comment: 4 pages RevTeX, 4 figure
Towards a strong-coupling theory of QCD at finite density
We apply strong-coupling perturbation theory to the QCD lattice Hamiltonian.
We begin with naive, nearest-neighbor fermions and subsequently break the
doubling symmetry with next-nearest-neighbor terms. The effective Hamiltonian
is that of an antiferromagnet with an added kinetic term for baryonic
"impurities," reminiscent of the t-J model of high-T_c superconductivity. As a
first step, we fix the locations of the baryons and make them static. Following
analyses of the t-J model, we apply large-N methods to obtain a phase diagram
in the (N_c,N_f) plane at zero temperature and baryon density. Next we study a
simplified U(3) toy model, in which we add baryons to the vacuum. We use a
coherent state formalism to write a path integral which we analyze with mean
field theory, obtaining a phase diagram in the (n_B,T) plane.Comment: Lattice2002(nonzerot) - Parallel talk and poster presented at Lattice
2002, Cambridge, MA, USA, June 2002. 6 pages, 6 EPS figure
Casimir scaling of domain wall tensions in the deconfined phase of D=3+1 SU(N) gauge theories
We perform lattice calculations of the spatial 't Hooft k-string tensions in
the deconfined phase of SU(N) gauge theories for N=2,3,4,6. These equal (up to
a factor of T) the surface tensions of the domain walls between the
corresponding (Euclidean) deconfined phases. For T much larger than Tc our
results match on to the known perturbative result, which exhibits Casimir
Scaling, being proportional to k(N-k). At lower T the coupling becomes stronger
and, not surprisingly, our calculations show large deviations from the
perturbative T-dependence. Despite this we find that the behaviour proportional
to k(N-k) persists very accurately down to temperatures very close to Tc. Thus
the Casimir Scaling of the 't Hooft tension appears to be a `universal' feature
that is more general than its appearance in the low order high-T perturbative
calculation. We observe the `wetting' of these k-walls at T around Tc and the
(almost inevitable) `perfect wetting' of the k=N/2 domain wall. Our
calculations show that as T tends to Tc the magnitude of the spatial `t Hooft
string tension decreases rapidly. This suggests the existence of a (would-be)
't Hooft string condensation transition at some temperature which is close to
but below Tc. We speculate on the `dual' relationship between this and the
(would-be) confining string condensation at the Hagedorn temperature that is
close to but above Tc.Comment: 40 pages, 14 figure
The large N limit of four dimensional Yang-Mills field coupled to adjoint fermions on a single site lattice
We consider the large N limit of four dimensional SU(N) Yang-Mills field
coupled to adjoint fermions on a single site lattice. We use perturbative
techniques to show that the Z^4_N center-symmetries are broken with naive
fermions but they are not broken with overlap fermions. We use numerical
techniques to support this result. Furthermore, we present evidence for a
non-zero chiral condensate for one and two Majorana flavors at one value of the
lattice gauge coupling.Comment: 21 pages, 13 figures; a reference added; version to be published in
JHEP, small clarifications and references adde
Electric Flux Tube in Magnetic Plasma
In this paper we study a methodical problem related to the magnetic scenario
recently suggested and initiated by the authors \cite{Liao_ES_mono} to
understand the strongly coupled quark-gluon plasma (sQGP): the electric flux
tube in monopole plasma. A macroscopic approach, interpolating between Bose
condensed (dual superconductor) and classical gas medium is developed first.
Then we work out a microscopic approach based on detailed quantum mechanical
calculation of the monopole scattering on electric flux tube, evaluating
induced currents for all partial waves. As expected, the flux tube looses its
stability when particles can penetrate it: we make this condition precise by
calculating the critical value for the product of the flux tube size times the
particle momentum, above which the flux tube dissolves. Lattice static
potentials indicate that flux tubes seem to dissolve at . Using our criterion one gets an estimate of the magnetic
density at this temperature.Comment: New version with new referecences added and minor changes. 15 pages,
8 figure
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