384 research outputs found
Anomaly and a QCD-like phase diagram with massive bosonic baryons
We study a strongly coupled lattice gauge theory with two flavors of
quarks, invariant under an exact symmetry which is the same as QCD with
two flavors of quarks without an anomaly. The model also contains a coupling
that can be used to break the symmetry and thus mimic the QCD
anomaly. At low temperatures and small baryon chemical potential
the model contains massless pions and massive bosonic baryons similar to QCD
with an even number of colors. In this work we study the phase
diagram of the model and show that it contains three phases : (1) A chirally
broken phase at low and , (2) a chirally symmetric baryon superfluid
phase at low and high , and (3) a symmetric phase at high . We
find that the nature of the finite temperature chiral phase transition and in
particular the location of the tricritical point that seperates the first order
line from the second order line is affected significantly by the anomaly.Comment: 22 pages, 16 figures, 5 tables, references adde
QCD-like theories at nonzero temperature and density
We investigate the properties of hot and/or dense matter in QCD-like theories
with quarks in a (pseudo)real representation of the gauge group using the
Nambu-Jona-Lasinio model. The gauge dynamics is modeled using a simple lattice
spin model with nearest-neighbor interactions. We first keep our discussion as
general as possible, and only later focus on theories with adjoint quarks of
two or three colors. Calculating the phase diagram in the plane of temperature
and quark chemical potential, it is qualitatively confirmed that the critical
temperature of the chiral phase transition is much higher than the
deconfinement transition temperature. At a chemical potential equal to half of
the diquark mass in the vacuum, a diquark Bose-Einstein condensation (BEC)
phase transition occurs. In the two-color case, a Ginzburg-Landau expansion is
used to study the tetracritical behavior around the intersection point of the
deconfinement and BEC transition lines, which are both of second order. We
obtain a compact expression for the expectation value of the Polyakov loop in
an arbitrary representation of the gauge group (for any number of colors),
which allows us to study Casimir scaling at both nonzero temperature and
chemical potential.Comment: JHEP class, 31 pages, 7 eps figures; v2: error in Eq. (3.11) fixed,
two references added; matches published versio
Numerical Study of the Two Color Attoworld
We consider QCD at very low temperatures and non-zero quark chemical
potential from lattice Monte Carlo simulations of the two-color theory in a
very small spatial volume (the attoscale). In this regime the quark number
rises in discrete levels in qualitative agreement with what is found
analytically at one loop on S3xS1 with radius R_S3 << 1/{\Lambda}_QCD. The
detailed level degeneracy, however, cannot be accounted for using weak coupling
arguments. At each rise in the quark number there is a corresponding spike in
the Polyakov line, also in agreement with the perturbative results. In addition
the quark number susceptibility shows a similar behaviour to the Polyakov line
and appears to be a good indicator of a confinement-deconfinement type of
transition.Comment: 18 pages, 10 figure
The sign problem across the QCD phase transition
The average phase factor of the QCD fermion determinant signals the strength
of the QCD sign problem. We compute the average phase factor as a function of
temperature and baryon chemical potential using a two-flavor NJL model. This
allows us to study the strength of the sign problem at and above the chiral
transition. It is discussed how the anomaly affects the sign problem.
Finally, we study the interplay between the sign problem and the endpoint of
the chiral transition.Comment: 9 pages and 9 fig
QCD with Chemical Potential in a Small Hyperspherical Box
To leading order in perturbation theory, we solve QCD, defined on a small
three sphere in the large N and Nf limit, at finite chemical potential and map
out the phase diagram in the (mu,T) plane. The action of QCD is complex in the
presence of a non-zero quark chemical potential which results in the sign
problem for lattice simulations. In the large N theory, which at low
temperatures becomes a conventional unitary matrix model with a complex action,
we find that the dominant contribution to the functional integral comes from
complexified gauge field configurations. For this reason the eigenvalues of the
Polyakov line lie off the unit circle on a contour in the complex plane. We
find at low temperatures that as mu passes one of the quark energy levels there
is a third-order Gross-Witten transition from a confined to a deconfined phase
and back again giving rise to a rich phase structure. We compare a range of
physical observables in the large N theory to those calculated numerically in
the theory with N=3. In the latter case there are no genuine phase transitions
in a finite volume but nevertheless the observables are remarkably similar to
the large N theory.Comment: 44 pages, 18 figures, jhep3 format. Small corrections and
clarifications added in v3. Conclusions cleaned up. Published versio
Classical Effective Field Theory for Weak Ultra Relativistic Scattering
Inspired by the problem of Planckian scattering we describe a classical
effective field theory for weak ultra relativistic scattering in which field
propagation is instantaneous and transverse and the particles' equations of
motion localize to the instant of passing. An analogy with the non-relativistic
(post-Newtonian) approximation is stressed. The small parameter is identified
and power counting rules are established. The theory is applied to reproduce
the leading scattering angle for either a scalar interaction field or
electro-magnetic or gravitational; to compute some subleading corrections,
including the interaction duration; and to allow for non-zero masses. For the
gravitational case we present an appropriate decomposition of the gravitational
field onto the transverse plane together with its whole non-linear action. On
the way we touch upon the relation with the eikonal approximation, some
evidence for censorship of quantum gravity, and an algebraic ring structure on
2d Minkowski spacetime.Comment: 29 pages, 2 figures. v4: Duration of interaction is determined in Sec
4 and detailed in App C. Version accepted for publication in JHE
Orbifold equivalence for finite density QCD and effective field theory
In the large N_c limit, some apparently different gauge theories turn out to
be equivalent due to large N_c orbifold equivalence. We use effective field
theory techniques to explore orbifold equivalence, focusing on the specific
case of a recently discovered relation between an SO(2N_c) gauge theory and
QCD. The equivalence to QCD has been argued to hold at finite baryon chemical
potential, \mu_B, so long as one deforms the SO(2N_c) theory by certain
"double-trace" terms. The deformed SO(2N_c) theory can be studied without a
sign problem in the chiral limit, in contrast to SU(N_c) QCD at finite \mu_B.
The purpose of the double-trace deformation in the SO(2N_c) theory is to
prevent baryon number symmetry from breaking spontaneously at finite density,
which is necessary for the equivalence to large N_c QCD to be valid. The
effective field theory analysis presented here clarifies the physical
significance of double-trace deformations, and strongly supports the proposed
equivalence between the deformed SO(2N_c) theory and large N_c QCD at finite
density.Comment: 39 pages, 5 figures, 2 tables. v2: Minor typo fixes and
clarification
The order of the quantum chromodynamics transition predicted by the standard model of particle physics
We determine the nature of the QCD transition using lattice calculations for
physical quark masses. Susceptibilities are extrapolated to vanishing lattice
spacing for three physical volumes, the smallest and largest of which differ by
a factor of five. This ensures that a true transition should result in a
dramatic increase of the susceptibilities.No such behaviour is observed: our
finite-size scaling analysis shows that the finite-temperature QCD transition
in the hot early Universe was not a real phase transition, but an analytic
crossover (involving a rapid change, as opposed to a jump, as the temperature
varied). As such, it will be difficult to find experimental evidence of this
transition from astronomical observations.Comment: 7 pages, 4 figure
Centre symmetric 3d effective actions for thermal SU(N) Yang-Mills from strong coupling series
We derive three-dimensional, Z(N)-symmetric effective actions in terms of
Polyakov loops by means of strong coupling expansions, starting from thermal
SU(N) Yang-Mills theory in four dimensions on the lattice. An earlier action in
the literature, corresponding to the (spatial) strong coupling limit, is thus
extended by several higher orders, as well as by additional interaction terms.
We provide analytic mappings between the couplings of the effective theory and
the parameters of the original thermal lattice theory, which can
be systematically improved. We then investigate the deconfinement transition
for the cases SU(2) and SU(3) by means of Monte Carlo simulations of the
effective theory. Our effective models correctly reproduce second order 3d
Ising and first order phase transitions, respectively. Furthermore, we
calculate the critical couplings and find agreement with
results from simulations of the 4d theory at the few percent level for
.Comment: 27 pages, 21 figures; final version published in JHEP; attached the
corresponding Erratum (ref. JHEP 1107:014,2011, DOI 10.1007/JHEP07(2011)014)
for ease of consultatio
Index Theorem and Overlap Formalism with Naive and Minimally Doubled Fermions
We present a theoretical foundation for the Index theorem in naive and
minimally doubled lattice fermions by studying the spectral flow of a Hermitean
version of Dirac operators. We utilize the point splitting method to implement
flavored mass terms, which play an important role in constructing proper
Hermitean operators. We show the spectral flow correctly detects the index of
the would-be zero modes which is determined by gauge field topology. Using the
flavored mass terms, we present new types of overlap fermions from the naive
fermion kernels, with a number of flavors that depends on the choice of the
mass terms. We succeed to obtain a single-flavor naive overlap fermion which
maintains hypercubic symmetry.Comment: 27 pages, 17 figures; references added, version accepted in JHE
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