A Note on AdS/CFT Dual of SL(2,Z) Action on 3D Conformal Field Theories with U(1) Symmetry

In this letter, we elaborate on the SL(2,Z) action on three dimensional conformal field theories with U(1) symmetry introduced by Witten, by trying to give an explicit verification of the claim regarding holographic dual of the S operation in AdS/CFT correspondence. A consistency check with the recently proposed prescription on boundary condition of bulk fields when we deform the boundary CFT in a non-standard manner is also discussed.Comment: LaTex, 1+15 pages, 1 figure, v2: discussion in terms of deformation theory is adde

Flows and polarization of early photons with magnetic field at strong coupling

Recent experimental results from RHIC and LHC on hard photon emission rates in heavy-ion collisions indicate a large azimuthal asymmetry of photon emission rate parameterized by the elliptic flow v_2. Motivated by a recent proposal that the early magnetic field created by two colliding heavy-ions may be responsible for this large azimuthal asymmetry of photon emission rate, we compute the azimuthal dependence of the photon emission rate from a strongly coupled finite temperature plasma with magnetic field in the framework of gauge/gravity correspondence. We also propose and compute a new observable, "in/out-plane polarization asymmetry", constructed from the polarization dependence of the photon emission rates. We observe that both the azimuthal and polarization asymmetry of photon emissions are strongly affected by the triangle anomaly (chiral anomaly) for low frequency regime below 1 GeV.Comment: 25 pages, 7 figure

Recent Theoretical Developments in Strongly Coupled QCD

Heavy-ion collisions involve strongly coupled dynamics of QCD in the entire history of time evolution. We review recent theoretical efforts to meet this challenge, focusing on the two approaches that the speaker has contributed to: 1) Holography or AdS/CFT correspondence, and 2) Symmetry protected phenomena such as those originating from triangle anomaly. The presentation is oriented to non-experts on these fields, and hence relies on intuitive pictures of the methods and the results, without going into specific details.Comment: 8 pages, Prepared for the proceeding of the conference "Quark Matter 2012", Washington DC, August 13-18, 201

Chiral Magnetic Effect at Weak Coupling with Relaxation Dynamics

We provide a resolution of an old issue in weak coupling computation of the Chiral Magnetic Effect (CME) current, where a free chiral fermion theory gives two different results depending on the order of the two limits, $\omega\rightarrow 0$ (frequency) and $k\rightarrow 0$ (spatial momentum). We first argue based on hydrodynamics that in any reasonable interacting theory of chiral fermions the non-commutativity between the two limits should be absent, and we demonstrate this at weak coupling regime in two different frameworks: kinetic theory in the relaxation time approximation, and diagrammatic computation with resummation of damping rate. In the latter computation, we also show that the "pinch" singularity, which would make the summation of ladder diagrams necessary as in the P-even correlation function, is absent in the relevant P-odd correlation function. The correct value of CME current is reproduced even in the presence of relaxation dynamics in both computations.Comment: 26 pages, 3 figure

Out-of-Equilibrium Chiral Magnetic Effect at Strong Coupling

We study the charge transports originating from triangle anomaly in out-of-equilibrium conditions in the framework of AdS/CFT correspondence at strong coupling, to gain useful insights on possible charge separation effects that may happen in the very early stages of heavy-ion collisions. We first construct a gravity background of a homogeneous mass shell with a finite (axial) charge density gravitationally collapsing to a charged blackhole, which serves as a dual model for out-of-equilibrium charged plasma undergoing thermalization. We find that a finite charge density in the plasma slows down the thermalization. We then study the out-of-equilibrium properties of Chiral Magnetic Effect and Chiral Magnetic Wave in this background. As the medium thermalizes, the magnitude of chiral magnetic conductivity and the response time delay grow. We find a dynamical peak in the spectral function of retarded current correlator, which we identify as an out-of-equilibrium chiral magnetic wave. The group velocity of the out-of-equilibrium chiral magnetic wave is shown to receive a dominant contribution from a non-equilibrium effect, making the wave moving much faster than in the equilibrium, which may enhance the charge transports via triangle anomaly in the early stage of heavy-ion collisions.Comment: 1+35 pages, 8 figures. References added. Published versio

Second Order Transport Coefficient from Chiral Anomaly at Weak Coupling: Diagrammatic Resummation

We compute one of the second order transport coefficients arising from the chiral anomaly in a high temperature weakly coupled regime of quark-gluon plasma. This transport coefficient is responsible for the CP-odd current that is proportional to the time derivative of the magnetic field, and can be considered as a first correction to the chiral magnetic conductivity at finite, small frequency. We observe that this transport coefficient has a non-analytic dependence on the coupling as $\sim 1/(g^4 \log(1/g))$ at weak coupling regime, which necessitates a re-summation of infinite ladder diagrams with leading pinch singularities to get a correct leading log result: a feature quite similar to that one finds in the computation of electric conductivity. We formulate and solve the relevant CP-odd Schwinger-Dyson equation in real-time perturbation theory that reduces to a coupled set of second order differential equations at leading log order. Our result for this second order transport coefficient indicates that chiral magnetic current has some resistance to the time change of magnetic field, which may be called "chiral induction effect". We also discuss the case of color current induced by color magnetic field.Comment: 54 pages, 8 figure