Abstract
We study the time evolution of the expectation value of a rectangular Wilson loop in strongly anisotropic time-dependent plasma using gauge-gravity duality. The corresponding gravity theory is given by describing time evolution of a classical string in the Lifshitz–Vaidya background. We show that the expectation value of the Wilson loop oscillates about the value of the static potential with the same parameters after the energy injection is over. We discuss how the amplitude and frequency of the oscillation depend on the parameters of the theory. In particular, for the transverse case, by raising the anisotropy parameter, we observe that the amplitude and frequency of the oscillation increase. In the longitudinal case, although the amplitude of the oscillation increases for larger values of anisotropy parameter, the frequency is independent of anisotropy parameter.
Highlights
Static potential energy is studied in different gauge theories with holographic duals and it recently generalizes to a time-dependent case in [14]
Holographic-ally, the mentioned system corresponds to the time evolution of the classical string in the AdS-Vaidya background
The AdS-Vaidya background is dual to thermalization process in the gauge theory [15]
Summary
We will give a brief review on the background used to calculate (time-dependent) expectation value of the Wilson-loop. The non-zero temperature Lifshitz-like metric is given by ds. The horizon is located at zh = m−ν/(2+2ν) and the Hawking temperature, corresponding to the temperature of the gauge theory, is given by T. and the metric approaches Lifshitz-like geometry asymptotically. The arbitrary function M(v), related to the temperature of the gauge theory, represents the mass of the black hole which changes as time passes by until it reaches a constant value. By universal behavior we mean the re-scaled equilibration time k−1teq is independent of the final value of the temperature. This result is perhaps common to all strongly coupled gauge theory with gravity dual.
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