199 research outputs found

### Aspects of the Color Flavor Locking phase of QCD in the Nambu-Jona Lasinio approximation

We study two aspects of the CFL phase of QCD in the NJL approximation. The
first one is the issue of the dependence on \mu of the ultraviolet cutoff in
the gap equation, which is solved allowing a running coupling constant. The
second one is the dependence of the gap on the strange quark mass; using the
high density effective theory we perform an expansion in the parameter
(m_s/\mu)^2 after checking that its numerical validity is very good already at
first order.Comment: LaTeX file, 6 figure

### Illuminating interfaces between phases of a U(1) x U(1) gauge theory

We study reflection and transmission of light at the interface between
different phases of a U(1) x U(1) gauge theory. On each side of the interface,
one can choose a basis so that one generator is free (allowing propagation of
light), and the orthogonal one may be free, Higgsed, or confined. However, the
basis on one side will in general be rotated relative to the basis on the other
by some angle alpha. We calculate reflection and transmission coefficients for
both polarizations of light and all 8 types of boundary, for arbitrary alpha.
We find that an observer measuring the behavior of light beams at the boundary
would be able to distinguish 4 different types of boundary, and we show how the
remaining ambiguity arises from the principle of complementarity
(indistinguishability of confined and Higgs phases) which leaves observables
invariant under a global electric/magnetic duality transformation. We also
explain the seemingly paradoxical behavior of Higgs/Higgs and confined/confined
boundaries, and clarify some previous arguments that confinement must involve
magnetic monopole condensation.Comment: RevTeX, 12 page

### Numerical solution of the color superconductivity gap in a weak coupling constant

We present the numerical solution of the full gap equation in a weak coupling
constant $g$. It is found that the standard approximations to derive the gap
equation to the leading order of coupling constant are essential for a secure
numerical evaluation of the logarithmic singularity with a small coupling
constant. The approximate integral gap equation with a very small $g$ should be
inverted to a soft integral equation to smooth the logarithmic singularity near
the Fermi surface. The full gap equation is solved for a rather large coupling
constant $g\ge 2.0$. The approximate and soft integral gap equations are solved
for small $g$ values. When their solutions are extrapolated to larger $g$
values, they coincide the full gap equation solution near the Fermi surface.
Furthermore, the analytical solution matches the numerical one up to the order
one O(1). Our results confirm the previous estimates that the gap energy is of
the order tens to 100 MeV for the chemical potential $\mu\le 1000$ MeV. They
also support the validity of leading approximations applied to the full gap
equation to derive the soft integral gap equation and its analytical solution
near the Fermi surface.Comment: 7 pages+ 6 figs, Stanford, Frankfurt and Bethlehe

### Spin-one color superconductivity in compact stars?- an analysis within NJL-type models

We present results of a microscopic calculation using NJL-type model of
possible spin-one pairings in two flavor quark matter for applications in
compact star phenomenology. We focus on the color-spin locking phase (CSL) in
which all quarks pair in a symmetric way, in which color and spin states are
locked. The CSL condensate is particularly interesting for compact star
applications since it is flavor symmetric and could easily satisfy charge
neutrality. Moreover, the fact that in this phase all quarks are gapped might
help to suppress the direct Urca process, consistent with cooling models. The
order of magnitude of these small gaps (~1 MeV) will not influence the EoS, but
their also small critical temperatures (T_c ~800 keV) could be relevant in the
late stages neutron star evolution, when the temperature falls below this value
and a CSL quark core could form.Comment: 7 pages, 7 figures, revised version, accepted for the Conference
Proceedings of "Isolated Neutron Stars: from the Interior to the Surface",
London, 24-28. April 200

### Instanton-induced crossover in dense QCD

We study the properties of an instanton ensemble in three-flavor dense QCD
which can be regarded as an instanton plasma weakly interacting by exchanging
the eta' mesons. Based on this description, we explore the chiral phase
transition induced by the instanton ensemble at high baryon density in analogy
with the Berezinskii-Kosterlitz-Thouless transition. Using the renormalization
group approach, we show that the instanton ensemble always behaves as a
screened and unpaired plasma. We also demonstrate that the chiral condensate in
dense QCD is proportional to the instanton density.Comment: 15 pages; version to appear in JHE

### Numerical Portrait of a Relativistic BCS Gapped Superfluid

We present results of numerical simulations of the 3+1 dimensional Nambu -
Jona-Lasinio (NJL) model with a non-zero baryon density enforced via the
introduction of a chemical potential mu not equal to 0. The triviality of the
model with a number of dimensions d>=4 is dealt with by fitting low energy
constants, calculated analytically in the large number of colors (Hartree)
limit, to phenomenological values. Non-perturbative measurements of local order
parameters for superfluidity and their related susceptibilities show that, in
contrast to the 2+1 dimensional model, the ground-state at high chemical
potential and low temperature is that of a traditional BCS superfluid. This
conclusion is supported by the direct observation of a gap in the dispersion
relation for 0.5<=(mu a)<=0.85, which at (mu a)=0.8 is found to be roughly 15%
the size of the vacuum fermion mass. We also present results of an initial
investigation of the stability of the BCS phase against thermal fluctuations.
Finally, we discuss the effect of splitting the Fermi surfaces of the pairing
partners by the introduction of a non-zero isospin chemical potential.Comment: 41 pages, 19 figures, uses axodraw.sty, v2: minor typographical
correction

### Breaking rotational symmetry in two-flavor color superconductors

The color superconductivity under flavor asymmetric conditions relevant to
the compact star phenomenology is studied within the Nambu-Jona-Lasinio model.
We focus on the effect of the deformation of the Fermi surfaces on the pairing
properties and the energy budget of the superconducting state. We find that at
finite flavor asymmetries the color superconducting BCS state is unstable
towards spontaneous quadrupole deformation of the Fermi surfaces of the $d$ and
$u$ quarks into ellipsoidal form. The ground state of the phase with deformed
Fermi surfaces corresponds to a superposition of prolate and oblate deformed
Fermi ellipsoids of $d$ and $u$ quarks.Comment: 6 pages, 4 figures. Parameter changes, references added, conclusions
unchange

### Positivity of High Density Effective Theory

We show that the effective field theory of low energy modes in dense QCD has
positive Euclidean path integral measure. The complexity of the measure of QCD
at finite chemical potential can be ascribed to modes which are irrelevant to
the dynamics at sufficiently high density. Rigorous inequalities follow at
asymptotic density. Lattice simulation of dense QCD should be possible using
the quark determinant calculated in the effective theory.Comment: 10 pages, Revised version, to appear in Rapid Communications of
Physical Review

### Strange Stars with a Density-Dependent Bag Parameter

We have studied strange quark stars in the framework of the MIT bag model,
allowing the bag parameter B to depend on the density of the medium. We have
also studied the effect of Cooper pairing among quarks, on the stellar
structure. Comparison of these two effects shows that the former is generally
more significant. We studied the resulting equation of state of the quark
matter, stellar mass-radius relation, mass-central-density relation,
radius-central-density relation, and the variation of the density as a function
of the distance from the centre of the star. We found that the
density-dependent B allows stars with larger masses and radii, due to
stiffening of the equation of state. Interestingly, certain stellar
configurations are found to be possible only if B depends on the density. We
have also studied the effect of variation of the superconducting gap parameter
on our results.Comment: 23 pages, 8 figs; v2: 25 pages, 9 figs, version to be published in
Phys. Rev. (D

### Quantumgroups in the Higgs Phase

In the Higgs phase we may be left with a residual finite symmetry group H of
the condensate. The topological interactions between the magnetic- and electric
excitations in these so-called discrete H gauge theories are completely
described by the Hopf algebra or quantumgroup D(H). In 2+1 dimensional space
time we may add a Chern-Simons term to such a model. This deforms the
underlying Hopf algebra D(H) into a quasi-Hopf algebra by means of a 3-cocycle
H. Consequently, the finite number of physically inequivalent discrete H gauge
theories obtained in this way are labelled by the elements of the cohomology
group H^3(H,U(1)). We briefly review the above results in these notes. Special
attention is given to the Coulomb screening mechanism operational in the Higgs
phase. This mechanism screens the Coulomb interactions, but not the
Aharonov-Bohm interactions. (Invited talk given by Mark de Wild Propitius at
`The III International Conference on Mathematical Physics, String Theory and
Quantum Gravity', Alushta, Ukraine, June 13-24, 1993. To be published in Theor.
Math. Phys.)Comment: 19 pages in Latex, ITFA-93-3

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