How the quark self-energy affects the color-superconducting gap

We consider color superconductivity with two flavors of massless quarks which form Cooper pairs with total spin zero. We solve the gap equation for the color-superconducting gap parameter to subleading order in the QCD coupling constant $g$ at zero temperature. At this order in $g$, there is also a previously neglected contribution from the real part of the quark self-energy to the gap equation. Including this contribution leads to a reduction of the color-superconducting gap parameter \f_0 by a factor b_0'=\exp \big[ -(\p ^2+4)/8 \big]\simeq 0.177. On the other hand, the BCS relation T_c\simeq 0.57\f_0 between \f_0 and the transition temperature $T_c$ is shown to remain valid after taking into account corrections from the quark self-energy. The resulting value for $T_c$ confirms a result obtained previously with a different method.Comment: Revtex, 8 pages, no figur

Functional Relation of interquark potential with interquark distance

The functional relation between interquark potential and interquark distance is explicitly derived by considering the Nambu--Goto action in the $AdS_5 \times S^5$ background. It is also shown that a similar relation holds in a general background. The implications of this relation for confinement are briefly discussed.Comment: 11pages, 2 figures, reference adde

QCD with chiral 4-fermion interactions (χ\chiQCD)

Lattice QCD with staggered quarks is augmented by the addition of a chiral 4-fermion interaction. The Dirac operator is now non-singular at $m_q=0$, decreasing the computing requirements for light quark simulations by at least an order of magnitude. We present preliminary results from simulations at finite and zero temperatures for $m_q=0$, with and without gauge fields.Comment: 3 pages. uuencoded, gzipped, tared LateX with 2 encapsulated postscript figures. Uses epscrc2.sty. Talk presented at LATTICE96(chirality in qcd). Title changed; minor changes at beginning and end of paper and reference

Hidden functional relation in Large-N Quark-Monopole system at finite temperature

The quark-monopole potential is computed at finite temperature in the context of $AdS/CFT$ correspondence. It is found that the potential is invariant under $g \to 1/g$ and $U_T \to U_T / g$. As in the quark-quark case there exists a maximum separation between quark and monopole, and $L$-dependence of the potential exhibits a bifurcation behavior. We find a functional relation $dE_{QM}^{Reg} / dL = [(1/E_{(1,0)}^{Reg}(U_0))^2 + (1/E_{(0,1)}^{Reg}(U_0))^2]^{-1/2}$ which is responsible for the bifurcation. The remarkable property of this relation is that it makes a relation between physical quantities defined at the $AdS$ boundary through a quantity defined at the bulk. The physical implication of this relation for the existence of the extra dimension is speculated.Comment: 22 pages, 3 figures, v1 one more reference added v2 version to appear in NP

Generalized Ward identity and gauge invariance of the color-superconducting gap

We derive a generalized Ward identity for color-superconducting quark matter via the functional integral approach. The identity implies the gauge independence of the color-superconducting gap parameter on the quasi-particle mass shell to subleading order in covariant gauge.Comment: 5 pages, 1 Postscript figure, uses Revte

Gluon self-energy in a two-flavor color superconductor

The energy and momentum dependence of the gluon self-energy is investigated in a color superconductor with two flavors of massless quarks. The presence of a color-superconducting quark-quark condensate modifies the gluon self-energy for energies which are of the order of the gap parameter. For gluon energies much larger than the gap, the self-energy assumes the form given by the standard hard-dense loop approximation. It is shown that this modification of the gluon self-energy does not affect the magnitude of the gap to leading and subleading order in the weak-coupling limit.Comment: 21 pages, 6 figures, RevTeX, aps and epsfig style files require

Magnetic catalysis and anisotropic confinement in QCD

The expressions for dynamical masses of quarks in the chiral limit in QCD in a strong magnetic field are obtained. A low energy effective action for the corresponding Nambu-Goldstone bosons is derived and the values of their decay constants as well as the velocities are calculated. The existence of a threshold value of the number of colors $N^{thr}_c$, dividing the theories with essentially different dynamics, is established. For the number of colors $N_c \ll N^{thr}_c$, an anisotropic dynamics of confinement with the confinement scale much less than $\Lambda_{QCD}$ and a rich spectrum of light glueballs is realized. For $N_c$ of order $N^{thr}_c$ or larger, a conventional confinement dynamics takes place. It is found that the threshold value $N^{thr}_c$ grows rapidly with the magnetic field [$N^{thr}_c \gtrsim 100$ for $|eB| \gtrsim (1{GeV})^2$]. In contrast to QCD with a nonzero baryon density, there are no principal obstacles for checking these results and predictions in lattice computer simulations.Comment: 10 pages, 1 figure. REVTeX. Minor correction. To appear in Phys. Rev.

Dynamics of Baryons from String Theory and Vector Dominance

We consider a holographic model of QCD from string theory, a la Sakai and Sugimoto, and study baryons. In this model, mesons are collectively realized as a five-dimensional \$U(N_F)=U(1)\times SU(N_F)$ Yang-Mills field and baryons are classically identified as $SU(N_F)$ solitons with a unit Pontryagin number and $N_c$ electric charges. The soliton is shown to be very small in the large 't Hooft coupling limit, allowing us to introduce an effective field ${\cal B}$. Its coupling to the mesons are dictated by the soliton structure, and consists of a direct magnetic coupling to the $SU(N_F)$ field strength as well as a minimal coupling to the $U(N_F)$ gauge field. Upon the dimensional reduction, this effective action reproduces all interaction terms between nucleons and an infinite tower of mesons in a manner consistent with the large $N_c$ expansion. We further find that all electromagnetic interactions, as inferred from the same effective action via a holographic prescription, are mediated by an infinite tower of vector mesons, rendering the baryon electromagnetic form factors completely vector-dominated as well. We estimate nucleon-meson couplings and also the anomalous magnetic moments, which compare well with nature.Comment: 65pages, 3 figures, vector mesons and axial-vector mesons are now canonically normalized (comparisons with data and conclusions unaffected

Dynamical Chiral Symmetry Breaking on the Light Front I. DLCQ Approach

Dynamical chiral symmetry breaking in the DLCQ method is investigated in detail using a chiral Yukawa model closely related to the Nambu-Jona-Lasinio model. By classically solving three constraints characteristic of the light-front formalism, we show that the chiral transformation defined on the light front is equivalent to the usual one when bare mass is absent. A quantum analysis demonstrates that a nonperturbative mean-field solution to the ``zero-mode constraint'' for a scalar boson (sigma) can develop a nonzero condensate while a perturbative solution cannot. This description is due to our identification of the ``zero-mode constraint'' with the gap equation. The mean-field calculation clarifies unusual chiral transformation properties of fermionic field, which resolves a seemingly inconsistency between triviality of the null-plane chiral charge Q_5|0>=0 and nonzero condensate. We also calculate masses of scalar and pseudoscalar bosons for both symmetric and broken phases, and eventually derive the PCAC relation and nonconservation of Q_5 in the broken phase.Comment: Revised version to appear in Phys. Rev. D. 19 pages, 4 figures, REVTEX. Derivation of the PCAC relation is given. Its relation to the nonconservation of chiral charge is clarified. 1 figure and some references adde