Chiral Magnetic Effect on the Lattice
We review recent progress on the lattice simulations of the chiral magnetic effect. There are two different approaches to analyze the chiral magnetic effect on the lattice. In one approach, the charge density distribution or the current fluctuation is mea
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Chiral Magnetic Effect on the Lattice Arata Yamamoto
15.1 Introduction In the strong interaction, the gauge field forms nontrivial topology. The existence of the topology has been theoretically established, while its observation is difficult in experiments. The chiral magnetic effect is a possible candidate to detect the topological structure in heavy-ion collisions [1]. The chiral magnetic effect is the generation of an electric current in a strong magnetic field. The essence of the chiral magnetic effect is the imbalance of the chirality, i.e., the number difference between the right-handed and left-handed quarks. The magnetic field induces the electric currents of the right-handed and left-handed quarks in opposite directions. If the chirality is imbalanced, a nonzero net electric current is induced. In a local domain of the QCD vacuum, the chiral imbalance is generated by the topological fluctuation and the axial anomaly. In the global QCD vacuum, the chirality is balanced as a whole. The strong theta parameter is experimentally zero, θ = 0, although its reason is unknown. This is the strong CP problem. The chiral magnetic effect is regarded as the local violation of the P and CP symmetries. Experimental facilities tried to measure the chiral magnetic effect through charged-particle correlations [2, 3]. However, the interpretation of the experimental data is not yet conclusive. On the theoretical side, the chiral magnetic effect has been studied in various frameworks, e.g., phenomenological models, the gaugegravity duality, etc. The chiral magnetic effect has been also studied in the lattice simulations. The lattice simulation is a powerful framework to solve QCD nonperturbatively on computers. By means of the lattice simulation, we can study the chiral magnetic effect from first principles in QCD.
A. Yamamoto (B) Quantum Hadron Physics Laboratory, Theoretical Research Division, RIKEN Nishina Center, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan e-mail: [email protected] D. Kharzeev et al. (eds.), Strongly Interacting Matter in Magnetic Fields, Lecture Notes in Physics 871, DOI 10.1007/978-3-642-37305-3_15, © Springer-Verlag Berlin Heidelberg 2013
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Fig. 15.1 A cartoon of how to observe the chiral magnetic effect on the lattice. Left: A topological charge Q of the gauge field induces a nonuniform current density distribution. Right: A chiral chemical potential μ5 induces a uniform electric current
There are two approaches to analyze the chiral magnetic effect in the lattice simulation. In other words, there are two different ways to generate the chiral imbalance: 1. topological charge [4–9] 2. chiral chemical potential [10–12] These concepts are schematically depicted in Fig. 15.1. In the first case, a topological charge of the background gauge field generates the chiral imbalance, which is spatially nonuniform. When an external magnetic field is applied, a current density distribution appears around the topological object. In the second case, a chiral chemical potential generates the
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