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The chiral magnetic effect with a fluctuating chiral imbalance is more realistic in the evolution of quark-gluon plasma, which reflects the random gluonic topological transition. Incorporating this dynamics, we calculate the chiral magnetic current in response to space-time dependent axial gauge potential and magnetic field in AdS/CFT correspondence. In contrast to conventional treatment of constant axial chemical potential, the response function here is the AVV three-point function of the $\mathcal{N}=4$ super Yang-Mills at strong coupling. Through an iterative solution of the nonlinear equations of motion in Schwarzschild-AdS$_5$ background, we are able to express the AVV function in terms of two Heun functions and prove its UV/IR finiteness, as expected for $\mathcal{N}=4$ super Yang-Mills theory. We found that the dependence of the chiral magnetic current on a non-constant chiral imbalance is non-local, different from hydrodynamic approximation, and demonstrates the subtlety of the infrared limit discovered in field theoretic approach. We expect our results enrich the understanding of the phenomenology of the chiral magnetic effect in the context of relativistic heavy ion collisions., Comment: 36 pages, 2 figure

The response of chiral fermions to time and space dependent axial imbalance & constant magnetic field is analyzed. The axialvector-vector-vector (AVV) three-point function is studied using a real-time approach at finite temperature in the weak external field approximation. The chiral magnetic conductivity is given analytically for noninteracting fermions. It is pointed out that local charge conservation plays an important role when the axial imbalance is inhomogeneous. Proper regularization is needed which makes the constant axial imbalance limit delicate: for static but spatially oscillating chiral charge the current of the chiral magnetic effect (CME) vanishes. In the homogeneous (but possible time-dependent) limit of the axial imbalance the CME current is determined solely by the chiral anomaly. As a phenomenological consequence, the observability of the charge asymmetry caused by the CME turns out to be a matter of interplay between various scales of the system. Possible plasma instabilities resulting from the gradient corrections to the CME current are also pointed out., 21 pages, 5 figures. v2: substantial changes of text, fig. 3 updated, practically matches journal version

We study in this paper the radiative corrections to chiral magnetic current at both zero and nonzero temperature. Our motivation is a radiative correction to the matrix element of the anomalous Ward identity in massless QED stemming from a three-loop diagram where the two photons coming from the one-loop anomalous triangle are re-scattered. Through the interplay between the Ward identity and the infrared subtlety of the fermion loop integral, we are able to reproduce the corrections known in literature in a simpler approach and obtain its contribution to the chiral magnetic current at zero temperature. At a nonzero temperature, the infrared subtlety disappeared in a static magnetic field and the three-loop diagram does not contribute to the chiral magnetic current any more. The generalization to all orders of the massless QED and the QCD corrections are discussed., 15 pages, 3 figures

We study analytically the one-loop contribution to the Chiral Magnetic Effect(CME) using lattice regularization with a Wilson fermion field. In the continuum limit, we find that the chiral magnetic current vanishes at nonzero temperature but emerges at zero temperature consistent with that found by Pauli-Villas regularization. For finite lattice size, however, the chiral magnetic current is nonvanishing at nonzero temperature. But the numerical vaule of the coefficient of CME current is very small compared with that extracted from the full QCD simulation for the same lattice parameters. The possibility of higher order corrections from QCD dynamics is also assessed., 7 pages

We calculate the magnetic polarization tensor of the photon and of the gluons in a two flavor color superconductor with a LOFF pairing that consists of a single plane wave. We show that at zero temperature and within the range of the values of the displacement of the Fermi sea that favors the LOFF state, all the eigenvalues of the magnetic polarization tensor are positive. Therefore the chromomagnetic instabilities pertaining to a gapless color superconductor disappear., Comment: 20 pages and 7 figures, Latex, typos were corrected, references added

We derive the quadratic action of the fluctuations around the classical world sheet underlying the jet quenching from AdS/CFT. After obtaining the correspondence partition function, the expansion of the jet quenching parameter of $\mathcal N=4$ super symmetric Yang-Mills theory is carried out to the sub-leading term in the large 't Hooft coupling $\lambda$ at a nonzero temperature. The strong coupling corresponds to the semi-classical expansion of the string-sigma model, the gravity dual of the Wilson loop operator, with the sub-leading term expressed in terms of functional determinants of fluctuations. The contribution of these determinants are evaluated numerically. We find the jet quenching parameter is reduced due to world sheet fluctuations by a factor $(1-1.97\lambda^{-1/2}) $, Comment: 34 pages, 2 figures, updated version accepted to be published in JHEP, with typos corrected and a few references added

Applying the AdS/CFT correspondence, the expansion of the heavy-quark potential of the N = 4 supersymmetric Yang-Mills theory at large Nc is carried out to the sub-leading term in the large ’t Hooft coupling at a nonzero temperature. The strong coupling corresponds to the semiclassical expansion of the string-sigma model, the gravity dual of the Wilson loop operator, with the sub-leading term expressed in terms of functional determinants of fluctuations. The contribution of these determinants are evaluated numerically. We also discuss some physics consequences of the subleading heavy quark potential.

For any purely fermionic system on a lattice in arbitrary space dimension we prove that there is a different but well-defined system on the same lattice, consisting of both bona fide fermions and bosons with an interaction depending on a parameter \ensuremath{\lambda}, which characterizes a same-site repulsion between particles. The energy spectrum and the scattering matrix of the former are identical to those in the finite energy sector of the latter, in the limit \ensuremath{\lambda}\ensuremath{\rightarrow}\ensuremath{\infty} (i.e., hard-core repulsion). This general theorem is applied to a resonance-boson model in a lattice fermion system, whose solution may have relevance to high-${\mathit{T}}_{\mathit{c}}$ superconductivity.

The nonzero strange quark mass effect in different types of single flavor color superconductivity and the phase diagram in a magnetic field are studied. We have obtained simple analytical forms of the quasi-particle energies for an arbitrary mass and explored the mass correction to the pressure and the transition temperature. It is found that the mass reduces the pressure and transition temperature of strange quarks, but it doesn't change the ranking $P_n, Comment: 16 pages in Revtex with 3 EPS-figures

In this paper, we shall address some field theoretic issues regarding the chiral magnetic effect. The general structure of the magnetic current consistent with the electromagnetic gauge invariance is obtained and the impact of the infrared divergence is examined. Some subtleties on the relation between the chiral magnetic effect and the axial anomaly are clarified through a careful examination of the infrared limit of the relevant thermal diagrams., Comment: 19 pages, 4 figures in Latex. Typos fixed, version accepted to be published in JHEP

Applying the AdS/CFT correspondence, the expansion of the heavy-quark potential of the ${\cal N}$ supersymmetric Yang-Mills theory at large $N_c$ is carried out to the sub-leading term in the large 't Hooft coupling at nonzero temperatures. The strong coupling corresponds to the semi-classical expansion of the string-sigma model, the gravity dual of the Wilson loop operator, with the sub-leading term expressed in terms of functional determinants of fluctuations. The contributions of these determinants are evaluated numerically., Comment: 17 pages in JHEP3, typos fixed, updated version to be published in JHEP

We examine the one-loop partition function describing the fluctuations of the superstring in a Schwarzschild-AdS{sub 5}xS{sup 5} background. On the bosonic side, we demonstrate the one-loop equivalence of the Nambu-Goto action and the Polyakov action for a general world sheet, while on the fermionic side, we consider the reduction of the ten-dimensional Green-Schwarz fermion action to a two-dimensional world sheet action. We derive the partition functions of the world sheets corresponding to both straight and parallel Wilson lines. We discuss the cancellation of the UV divergences of the functional determinants in the thermal AdS background.

We study the Anderson localization effect on the shear viscosity in a system with random medium by Kubo formula. We show that this effect can suppress nonperturbatively the shear viscosity and other transport coefficients. The possible relevancy of such a suppression to the near perfect fluid behavior of the quark-gluon plasma created in heavy-ion collisions is discussed.

The fluctuations of the Higgs and pseudo Nambu-Goldstone fields in the 2SC phase with mismatched pairing are described in the nonlinear realization framework of the gauged Nambu--Jona-Lasinio model. In the gapless 2SC phase, not only Nambu-Goldstone currents can be spontaneously generated, but the Higgs field also exhibits instablity. The Nambu-Goldstone currents generation indicates the formation of the single plane wave LOFF state and breaks rotation symmetry, while the Higgs instability favors spatial inhomogeneity and breaks translation invariance. In this paper, we focus on the Higgs instability which has not drawn much attention yet. The Higgs instability cannot be removed without a long range force, thus it persists in the gapless superfluidity and induces phase separation. In the case of g2SC state, the Higgs instability can only be partially removed by the electric Coulomb energy. However, it is not excluded that the Higgs instability might be completely removed in the charge neutral gCFL phase by the color Coulomb energy., 21 pages, 5 figures

The quarkonium states in a quark-gluon plasma is examined with the heavy quark potential implied by the holographic principle. Both the vanila AdS-Schwarzschild metric and the one with an infrared cutoff are considered. The dissociation temperature is calculated by solving the Schr\"o dinger equation of the potential model. In the case of the AdS-Schwarzschild metric with a IR cutoff, the dissociation temperatures for $J/\psi$ and $\Upsilon$ with the U-ansatz of the potential are found to agree with the lattice results within a factor of two., Comment: 9 pages with 2 figues in Revtex

In this letter we explore the Higgs instability in the gapless superfluid/superconducting phase. This is in addition to the (chromo)magnetic instability that is related to the fluctuations of the Nambu-Goldstone bosonic fields. While the latter may induce a single-plane-wave LOFF state, the Higgs instability favors spatial inhomogeneity and cannot be removed without a long range force. In the case of the g2SC state the Higgs instability can only be partially removed by the electric Coulomb energy. But this does not exclude the possibility that it can be completely removed in other exotic states such as the gCFL state., 4 pages, 2 figure, one figure added

We study the effects of gauge-field fluctuations on the free energy of a homogeneous color superconductor in the color-flavor-locked (CFL) phase. Gluonic fluctuations induce a strong first-order phase transition, in contrast to electronic superconductors where this transition is weakly first order. The critical temperature for this transition is larger than the one corresponding to the diquark pairing instability. The physical reason is that the gluonic Meissner masses suppress long-wavelength fluctuations as compared to the normal conducting phase where gluons are massless, which stabilizes the superconducting phase. In weak coupling, we analytically compute the temperatures associated with the limits of metastability of the normal and superconducting phases, as well as the latent heat associated with the first-order phase transition. We then extrapolate our results to intermediate densities and numerically evaluate the temperature of the fluctuation-induced first-order phase transition, as well as the discontinuity of the diquark condensate at the critical point. We find that the London limit of magnetic interactions is absent in color superconductivity., Comment: 14 pages, 5 figures

Type-I color superconductors display a first-order phase transition due to thermal gauge-field fluctuations. We numerically evaluated the critical temperature of the first-order phase transition and the corresponding discontinuity of the diquark condensate at the critical point., 4 pages, 1 figure, to appear in the proceedings of 18th International Conference on Ultrarelativistic Nucleus-Nucleus Collisions: Quark Matter 2005 (QM 2005), Budapest, Hungary, 4-9 Aug 2005, grant information updated, no other changes

In this paper we construct analytically a LOFF color superconducting state that is both color and charge neutral using the weak coupling approximation. We demonstrate that this state is free from chromomagnetic instabilities. Its relevance to the realistic quark matter at moderately high baryon density is discussed., 9 pages, Latex, correction of algebraic mistake and typos

We study the gauge field fluctuations in dense quark matter and determine the temperature of the induced first-order phase transition to the color-superconducting phase in weak coupling. We find that the local approximation of the coupling between the gauge potential and the order parameter, employed in the Ginzburg-Landau theory, has to be modified by restoring the full momentum dependence of the polarization function of gluons in the superconducting phase., Comment: 5 pages, 1 figure, Revtex, we have modified our conclusions for the metallic superconductor

We explore the relation between the chromomagnetic instability of a homogeneous two flavor color superconductor and the LOFF state. We perturb the free energy of the 2SC by generating a small net momentum for the quark pair. We find that the imaginary Meissner mass of a particular gluon implies that the LOFF state is energetically favored., Comment: 11 pages, no figures, latex, discussion on charge neutrality, new references were added

The Weyl-gauge ($A_0^a=0)$ QCD Hamiltonian is unitarily transformed to a representation in which it is expressed entirely in terms of gauge-invariant quark and gluon fields. In a subspace of gauge-invariant states we have constructed that implement the non-Abelian Gauss's law, this unitarily transformed Weyl-gauge Hamiltonian can be further transformed and, under appropriate circumstances, can be identified with the QCD Hamiltonian in the Coulomb gauge. We demonstrate an isomorphism that materially facilitates the application of this Hamiltonian to a variety of physical processes, including the evaluation of $S$-matrix elements. This isomorphism relates the gauge-invariant representation of the Hamiltonian and the required set of gauge-invariant states to a Hamiltonian of the same functional form but dependent on ordinary unconstrained Weyl-gauge fields operating within a space of ``standard'' perturbative states. The fact that the gauge-invariant chromoelectric field is not hermitian has important implications for the functional form of the Hamiltonian finally obtained. When this nonhermiticity is taken into account, the ``extra'' vertices in Christ and Lee's Coulomb-gauge Hamiltonian are natural outgrowths of the formalism. When this nonhermiticity is neglected, the Hamiltonian used in the earlier work of Gribov and others results., Comment: 25 pages

At sufficiently high baryon densities, the physics of a dense quark-gluon plasma may be investigated through the tools of perturbative QCD. This approach has recently been successfully applied to the study of color superconductivity, where the dominant di-quark pairing interaction arises from one gluon exchange. Screening in the plasma leads to novel behavior, including a remarkable non-BCS scaling of ${T}_{C},$ the transition temperature to the color superconducting phase. Radiative corrections to one gluon exchange were previously considered and found to affect ${T}_{C}.$ In particular, the quark self-energy in a plasma leads to non-Fermi liquid behavior and suppresses ${T}_{C}.$ However, at the same time, the quark-gluon vertex was shown not to modify the result at leading order. This dichotomy between the effects of the radiative corrections at first appears rather surprising, as the BRST identity connects the self-energy to the vertex corrections. Nevertheless, as we demonstrate, there is in fact no contradiction with the BRST identity, at least to leading logarithmic order. This clarifies some of the previous statements on the importance of the higher order corrections to the determination of ${T}_{C}$ and the zero temperature gap in color superconductivity.

Color superconductivity is a possible phase of high density QCD. We present a systematic derivation of the transition temperature T{sub C} from the QCD Lagrangian through study of the di-quark proper vertex. With this approach, we confirm the dependence of T{sub C} on the coupling g, namely T{sub C}{approx}{mu}g{sup -5}e{sup -{kappa}}{sup /g}, previously obtained from the one-gluon exchange approximation in the superconducting phase. The diagrammatic approach we employ allows us to examine the perturbative expansion of the vertex and the propagators. We find an additional O(1) contribution to the prefactor of the exponential from the one-loop quark self energy and that the other one-loop radiative contributions and the two gluon exchange vertex contribution are subleading. (c) 2000 The American Physical Society.

We expand the gauge field in terms of a suitably constructed complete set of Bloch wave functions, each labeled by a band designation $\,n\,$ and a wave number $\,\vec K\,$ restricted to the Brillouin zone. A noncompact formulation of lattice QCD (or QED) can be derived by restricting the expansion only to the $\,0^{th}$-band ($\,n = 0\,$) functions, which are simple continuum interpolations of discrete values associated with sites or links on a lattice. The exact continuum theory can be reached through the inclusion of all $\,n = 0\,$ and $\,n \ne 0\,$ bands, without requiring the lattice size $\,\ell \to 0\,$. This makes it possible, at a nonzero $\,\ell\,$, for the lattice coupling $\,g_\ell\,$ to act as the renormalized continuum coupling. All physical results in the continuum are, of course, independent of $\,\ell\,$., 72 pages, 3 Postscript figures

Applying the AdS/CFT correspondence, the expansion of the heavy-quark potential of the ${\cal N}=4$ supersymmetric Yang-Mills theory at large $N_c$ is carried out to the sub-leading term in the large 't Hooft coupling at zero temperature. The strong coupling corresponds to the semi-classical expansion of the string-sigma model, the gravity dual of the Wilson loop operator, with the sub-leading term expressed in terms of functional determinants of fluctuations. The singularities of these determinants are examined and their contributions are evaluated numerically., Updated version with minor typo corrections and new references

The quarkonium states in a quark-gluon plasma is examined with the potential implied by AdS/CFT duality. Both the vanila AdS-Schwarzschild metric and the one with an infrared cutoff are considered. The calculated dissociation temperatures for $J/\psi$ and $\Upsilon$ are found to agree with the lattice results within a factor of two., Comment: 6 pages with 3 tables in Latex, contribution to the proceedings of Strange quark matter 2008, Beijing, Oct. 5, 2008

The formulations of the scalar, spinor and gauge fields on a curved random lattice are discussed. A new fermion scheme — simplicial fermions — which is more natural in the presence of gravity, is introduced. Some of the propagators in D = 2 are evaluated numerically and are compared with the continuum limit.

Fermion propagators on a four-dimensional random lattice are calculated numerically. They show correct continuum limits. We also show that with the use of the point-splitting technique the composite boson propagators also approach the correct continuum limits.

The massless fermion field in two dimensions is studied on random lattices. By averaging over an ensemble of random lattices, it is shown that the chiral fermion propagators with or without an external abelian gauge field agree well with the continuum limit. Using the point-splitting definition, the composite boson propagators agree roughly with the continuum limit. The chiral symmetry and relevant anomalies are discussed.

The anomalies of chiral gauge theories are discussed from the point of view of point-splitting regularization. The integrability of the regularized current is examined. Its relations with the Wess-Zumino consistency condition and Bose symmetry of the regularized Feynman diagrams are discussed. A point-splitting regularization scheme of the action is proposed as an alternative way to calculate the consistent anomalies.

Hiroshi ITOYAMA Physics Department, Columbia University, New York, NY 10027, USA V.P. NAIR and Hai-cang REN Institute for Advanced Study, Princeton, NJ 08540, USA Received 1 May 1985 We show how the 5e-matrix elements avoid the problem of supersymmetry breaking by the gauge fixing and ghost terms for renormalization in the Wess-Zumino gauge. Possible origins of supersymmetry anomalies are discussed. Gauge and gravitational anomalies induce a supersym- metry anomaly which has two distinct terms, one of which is gauge invariant. We give the expression for the noninvariant term for 2n-dimensional spacetime and for the invariant part in four dimensions. This anomaly, although cohomologically nontrivial, is still consistent with the result that in superspace no supersymmetry anomaly is generated.

The SU(2) gauge theory on an 8 4 random lattice has been studied by the Monte Carlo method. The string tensions have been evaluated. They display the expected scaling behavior for β =1.2−1.3. The scale parameter Λ RAN has been determined approximately.

On etudie les modes zeros d'une action fermion sur un reseau aleatoire. On calcule les valeurs propres basses de l'action et on discute leur distribution

The finite temperature properties of SU(2) gauge fields on a random lattice are studied by the Monte Carlo method. The results indicate the existence of a deconfining transition at high temperature. The scale parameter of the random lattice is estimated.

The ensemble averages of various propagators of a free-fermion system on random lattices in D = 1 and D = 2 are calculated numerically. The results indicate a correct continuum limit. The cancellation mechanism of the unphysical states is investigated.

The SU(3) gauge theory on a random lattice is studied using the Monte Carlo method. The string tensions are measured. A scaling window around g0−2 = 1.4 is detected and the scale parameter is estimated.