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Chiral magnetic effect at low temperature

We investigate the chiral magnetic effect (CME) under a strong magnetic field B = B_0 x_3 at low temperature T < T^chi_c. For this purpose, we employ the instanton vacuum configuration with the finite instanton-number fluctuation Delta, which relates to the nontrivial topological charge Q_t. We compute the vacuum expectation values of the local chiral density <rho_chi>, chiral charge density <n_chi> and induced electromagnetic current <j_mu>, which signal the CME, as functions of T and B_0. We observed that the longitudinal EM current is much larger than the transverse one, |j_perp/j_parallel| ~ Q_t, and the <n_chi> equals to the |<j_{3,4}>|. It also turns out that the CME becomes insensitive to the magnetic field as T increases, according to the decreasing instanton, i.e. tunneling effect. Within our framework, the instanton contribution to the CME becomes almost negligible beyond T~300 MeV.