Jet quenching and holographic thermalization with a chemical potential

Abstract

Abstract:We investigate jet quenching of virtual gluons and thermalization of a stronglycoupled plasma with a non-zero chemical potential via the gauge/gravity duality. By tracking a charged shell falling in an asymptotic AdS d+1 background for d = 3 and d = 4, which is characterized by the AdS-Reissner-Nordström-Vaidya (AdS-RN-Vaidya) geometry, we extract a thermalization time of the medium with a non-zero chemical potential. In addition, we study the falling string as the holographic dual of a virtual gluon in the AdS-RN-Vaidya spacetime. The stopping distance of the massless particle representing the tip of the falling string in such a spacetime could reveal the jet quenching of an energetic light probe traversing the medium in the presence of a chemical potential. We find that the stopping distance decreases when the chemical potential is increased in both AdS-RN and AdS-RN-Vaidya spacetimes, which correspond to the thermalized and thermalizing media respectively. Moreover, we find that the soft gluon with an energy comparable to the thermalization temperature and chemical potential in the medium travels further in the non-equilibrium plasma. The thermalization time obtained here by tracking a falling charged shell does not exhibit, generically, the same qualitative features as the one obtained studying non-local observables. This indicates that -holographically -the definition of thermalization time is observer dependent and there is no unambiguos definition.

Holographic thermalization of charged operators

“…This energy condition (2.32) was discussed in [23][24][25][26]. We would like to remark that (2.32) coincides with the condition for the horizon not the recede.…”

“…The aforementioned results were generalized in [23][24][25][26] to situations with a non-trivial chemical potential or, in the dual perspective, to the case in which the system experiences a sudden injection of both energy and particles. The dual geometry was chosen to be that of a charged collapsing null shell interpolating between AdS in the distant past and asymptotically AdS Reissner-Nordstrom black hole (AdSRN) in the distant future.…”

“…The thermalization was probed by two point functions of chargeless operators, Wilson loops, and entanglement entropy. The emergent picture of [23][24][25] was that as the final chemical potential is increased, it takes longer for the system to thermalize (see [27]- [51] for related works).…”

“…isfying null energy conditions, in the present work we analyze the energy conditions of the previously explored charged Vaidya geometries [23][24][25][26] and its further generalizations. We afterwards study the thermalization process by probing the system with charged operators.…”

“…The organization of the paper is the following: in section 2 we analyze whether the Vaidya metric used in [23][24][25][26], that represents a quench on the chemical potential and temperature in the dual field theory, is supported by matter satisfying null energy conditions, in section 3 we probe the thermalization process with two point functions of charged operators. The results are presented and discussed in section 4.…”