Vacuum Instability in Electric Fields via AdS/CFT: Euler-Heisenberg Lagrangian and Planckian Thermalization

TL;DR

This paper investigates vacuum decay in strongly coupled gauge theories under electric fields using AdS/CFT, revealing a universal thermalization process with a Planckian timescale that aligns with experimental observations.

Contribution

It introduces a non-perturbative analysis of vacuum instability and thermalization in strongly coupled gauge theories via AdS/CFT, connecting decay rates to Schwinger effects and identifying a universal thermalization timescale.

Findings

Decay rate becomes nonzero above a critical electric field.

Thermalization occurs at a universal Planckian timescale inversely proportional to the square root of the electric field.

Predicted thermalization time matches experimental values in RHIC.

Abstract

We analyze vacuum instability of strongly coupled gauge theories in a constant electric field using AdS/CFT correspondence. The model is the N=2 1-flavor supersymmetric large N_c QCD in the strong 't Hooft coupling limit. We calculate the Euler-Heisenberg effective Lagrangian L(E), which encodes the nonlinear response and the quantum decay rate of the vacuum in a background electric field E, from the complex D-brane action in AdS/CFT. We find that the decay rate given by Im L(E) becomes nonzero above a critical electric field set by the confining force between quarks. A large-E expansion of Im L(E) is found to coincide with that of the Schwinger effects in QED, replacing its electron mass by the confining force. Then, the time-dependent response of the system in a strong electric field is solved non-perturbatively, and we observe a universal thermalization at a shortest timescale "Planckian thermalization time" t ~ 1/T ~ E^{-1/2}. Here, T is an effective temperature which quarks feel in the nonequilibrium state with nonzero electric current, calculated in AdS/CFT as a Hawking temperature. Stronger electric fields accelerate the thermalization, and for a realistic value of the electric field in RHIC experiment, we obtain t ~ 1 [fm/c], which is consistent with the believed value.