Chiral transport in strong fields from holography
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Springer
Received: March 18, 2019 Accepted: May 7, 2019 Published: May 14, 2019
Yanyan Bu,a Tuna Demircikb and Michael Lublinskyb a
Department of Physics, Harbin Institute of Technology, Harbin 150001, China b Department of Physics, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel
E-mail: [email protected], [email protected], [email protected] Abstract: Anomaly-induced transport phenomena in presence of strong external electromagnetic fields are explored within a 4D field theory defined holographically as U(1) V × U(1)A Maxwell-Chern-Simons theory in Schwarzschild-AdS5 . Two complementary studies are reported. In the first one, we present results on the Ohmic conductivity, diffusion constant, chiral magnetic conductivity, and additional anomaly-induced transport coefficients as functions of external e/m fields. Next, gradient resummation in a constant background magnetic field is performed. All-order resummed constitutive relations are parameterised by four momenta-dependent transport coefficient functions (TCFs). A highlight of this part is a thorough study of non-dissipative chiral magnetic waves (CMW) in strong magnetic fields. Keywords: AdS-CFT Correspondence, Gauge-gravity correspondence, Holography and condensed matter physics (AdS/CMT), Holography and quark-gluon plasmas ArXiv ePrint: 1903.00896
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP05(2019)071
JHEP05(2019)071
Chiral transport in strong fields from holography
Contents 1 1 3 5
2 Holographic setup: U(1)V × U(1)A
6
3 Part I: gradient expansion in external e/m fields 3.1 Constitutive relations at zeroth order ~ 6= 0, E ~ =0 3.2 Constitutive relations at first order — B ~ 6= 0, B ~ =0 3.3 Constitutive relations at first order — E
8 8 12 14
4 Part II: gradient resummation in external magnetic field 4.1 Derivation of the all-order resummed constitutive relations 4.2 The TCFs 4.3 Non-dissipative CMW modes
15 15 18 21
5 Concluding remarks
23
1 1.1
Introduction and summary Motivation
We continue exploring transport phenomena induced by chiral anomaly in a chiral plasma with both left- and right-handed U(1) (electrically) charged fermions. The microscopic theory is defined holographically: U(1)V × U(1)A Maxwell-Chern-Simons theory in Schwarzschild-AdS5 [1, 2] to be introduced in section 2. Transport phenomena for this theory have already been extensively studied by us [3–6], and by other authors [1, 2, 7]. Here ~ and B). ~ we primarily focus on some new results related to strong external e/m fields (E Realistic plasmas such as quark-gluon plasma produced in heavy ion collisions or primordial plasma in the early universe are exposed to strong external e/m fields. Furthermore, the dynamics of these plasmas is governed by magneto-hydrodynamics (MHD) which generates the fields dynamically, frequently resulting in even stronger fields [8–13]. Chiral anomaly is known to modify the MHD equations, turning them into chiral MHD. An essential ingredient of any hydrodynamics is constitutive relations
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