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Hai-cang Ren

Publications and source records attributed to Hai-cang Ren.

At least 19 recordsLinked to original sources
arXiv2021

Chiral Magnetic Effect and Three-point Function from AdS/CFT Correspondence

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.

hep-th↗
arXiv2020

The noncommutativity of the static and homogeneous limit of the axial chemical potential in chiral magnetic effect

We study the noncommutativity of different orders of zero energy-momentum limit pertaining to the axial chemical potential in the chiral magnetic effect. While this noncommutativity issue originates from the pinching singularity at one-loop order, it cannot be removed by introducing a damping term to the fermion propagators. The physical reason is that modifying the propagator alone would violate the axial-vector Ward identity and as a result a modification of the longitudinal component of the axial-vector vertex is required, which contributes to CME. The pinching singularity with free fermion propagators was then taken over by the singularity stemming from the dressed axial-vector vertex. We show this mechanism by a concrete example. Moreover, we proved in general the vanishing CME in the limit order that the static limit was taken prior to the homogeneous limit in the light of Coleman-Hill theorem for a static external magnetic field. For the opposite limit that the homogeneous limit is taken first, we show that the nonvanishing CME was a consequence of the nonrenormalizability of chiral anomaly for an arbitrary external magnetic field.

hep-ph↗
arXiv2020

Chiral magnetic response to arbitrary axial imbalance

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.

hep-ph↗
arXiv2019

Non-static Analysis of the Anomalous Chiral Conductivities

Given the intrinsic nonequilibrium nature of high-energy collisions the investigation of the dynamical properties of transport phenomena is important. The study of the real-time behavior of various conductivities and susceptibilities help refine the simulation tools we use to compare the theories and the experimental findings. In this contribution we take steps to give the chiral magnetic conductivity in case of magnetic field and chiral imbalance are both space-time dependent. Using linear response approximation we present the general 1-loop resummed expression for the electric current. We also suggest simple limiting cases in hope for possible implementation into a hydrodynamical framework.

hep-ph↗
arXiv2019

Holographic Magnetic Susceptibility

The (2+1)-dimensional static magnetic susceptibility in strong-coupling is studied via a Reissner-Nordström-AdS geometry. The analyticity of the susceptibility on the complex momentum $\mathfrak{q}$-plane in relation to the Friedel-like oscillation in coordinate space is explored. In contrast to the branch-cuts crossing the real momentum-axis for a Fermi liquid, we prove that the holographic magnetic susceptibility remains an analytic function of the complex momentum around the real axis in the limit of zero temperature, At zero temperature, we located analytically two pairs of branch-cuts that are parallel to the imaginary momentum-axis for large $|\text{Im}\ \mathfrak{q}|$ but become warped with the end-points keeping away from the real and imaginary momentum-axes. We conclude that these branch-cuts give rise to the exponential decay behaviour of Friedel-like oscillation of magnetic susceptibility in coordinate space. We also derived the analytical forms of the susceptibility in large and small-momentum, respectively.

hep-th↗
arXiv2018

The QED Radiative Corrections to Chiral Magnetic Effect

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.

hep-ph↗
arXiv2017

Momentum analyticity of the holographic electric polarizability in 2+1 dimensions

The static electric polarization of a holographic field theory dual to the Einstein-Maxwell theory in the background of $AdS_4$ with a Reissner-Nordstöm (AdS-RN) black hole is investigated. We prove that the holographic polarization is a meromorphic functions in complex momentum plane and locate analytically the asymptotic distribution of the poles along two straight lines parallel to the imaginary axis for a large momentum magnitude. The results are compared with the numerical result on Friedel-like poles of the same holographic model reported in the literature and with the momentum singularities of the one-loop polarization in weak-coupling spinor QED$_3$ and scalar QED$_3$ with the similarities and differences discussed.

hep-th↗
arXiv2017

Chiral Magnetic Effect in a Lattice Model

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.

hep-ph↗
arXiv2017

The Subtleties of the Wigner Function Formulation of the Chiral Magnetic Effect

We assess the applicability of the Wigner function formulation in its present form to the chiral Magnetic Effect and noted some issues regarding the conservation and the consistency of the electric current in the presence of an inhomogeneous and time dependent axial chemical potential. The problems are rooted in the ultraviolet divergence of the underlying field theory associated with the axial anomaly and can be fixed with the Pauli-Villars regularization of the Wigner function.

hep-ph↗
arXiv2016

Momentum Analyticity of Transverse Polarization Tensor in the Normal Phase of a Holographic Superconductor

We explore the momentum analyticity of the static transverse polarization tensor of a 2+1 dimensional holographic superconductor in its normal phase with a nonzero chemical potential, aiming at finding the holographic counterpart of the singularities underlying the Friedel-like oscillations of an ordinary field theory. We prove that the polarization tensor is a meromorphic function with an infinite number of poles located on the complex momentum plane off real axis. With the aid of the WKB approximation these poles are found to lies asymptotically along two straight lines parallel to the imaginary axis for a large momentum magnitude. The similarity between the holographic Green's function and that of an weakly coupled ordinary field theory (e.g., 2+1 dimensional QED) regarding the location of the momentum singularities offers further support to the validity of the gauge/gravity duality.

hep-th↗
arXiv2016

Bose-Einstein Condensation of Bound Pairs of Relativistic Fermions in a Magnetic Field

The Bose-Einstein condensation of bound pairs made of equally and oppositely charged fermions in a magnetic field is investigated using a relativistic model. The Gaussian fluctuations have been taken into account in order to study the spectrum of bound pairs in the strong coupling region. We found, in weak coupling reagion, the condensation temperature increases with an increasing magnetic field displaying the magnetic catalysis effect. In strong coupling region, the inverse magnetic catalysis appears when the magnetic field is low and is replaced by the usual magnetic catalysis effect when magnetic field is sufficiently high, in contrast to the nonrelativistic case where the inverse magnetic catalysis prevails in strong coupling region regardless of the strength of the magnetic field. The resulting response to the magnetic field is the consequence of the competition between the dimensional reduction by Landau orbitals in pairing dynamics and the anisotropy of the kinetic spectrum of the bound pairs. We thus conclude that dimensional reduction dominates in weak domain and strong coupling one except the small magnetic field region, where the enhanced fluctuations dominates.

hep-ph↗
arXiv2015

(Inverse) Magnetic Catalysis in Bose-Einstein Condensation of Neutral Bound Pairs

The Bose-Einstein condensation of bound pairs made of oppositely charged fermions in a magnetic field is investigated. We find that the condensation temperature shows the magnetic catalysis effect in weak coupling and the inverse magnetic catalysis effect in strong coupling. The different responses to the magnetic field can be attributed to the competition between the dimensional reduction by Landau orbitals in pairing dynamics and the anisotropy of the kinetic spectrum of fluctuations (bound pairs in the normal phase)

cond-mat.quant-gas↗
arXiv2014

The Ginzburg-Landau Theory of a Holographic Superconductor

The general Ginzburg-Landau formulation of a holographic superconductor is developed near the transition temperature in the probe limit for two kinds of conformal dimension. Below the transition temperature, $T<T_c$, the order-parameter scales with $\sqrt{1-\frac{T}{T_c}}$ as expected. The G-L free energy in grand caonnical ensemble and canonical ensemble are derived and the gradient term is studied. Furthermore this scaling coefficient of order-parameter takes different values in the grand canonical ensemble and the canonical ensemble, suggesting the strong coupling nature of the boundary field theory of the superconductiviy.

hep-th↗
arXiv2014

Some Comments on the Holographic Heavy Quark Potential in a Thermal Bath

The heavy quark potential of a thermal Yang-Mills theory in strong coupling limit is explored in terms of the holographic principle. With a fairly general AdS/QCD metric the heavy quark potential displays a kink-like screening in the plasma phase. This behavior may conflict the causality of a field theory that is mathematically equivalent to the thermal Yang-Mills.

hep-ph↗
arXiv2012

The finite 't Hooft coupling correction on the jet quenching parameter in a $\mathcal N=4$ Super Yang-Mills Plasma

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 $λ$ 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 $(1-1.97λ^{-1/2}) $

hep-th↗
arXiv2011

Mass Effect in Single Flavor Color 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 $P_n<P_{\rm A}<P_{\rm polar}<P_{\rm planar}<P_{\rm CSL}$ of the pressure for the four canonical single flavor phases. The phase diagram with magnetic field and temperature for a system of three flavors is obtained for two different values of the strange quark mass. The changes from the one obtained previously under the approximation of massless strange quarks are examined.

nucl-th↗