Abstract
Using the AdS/CFT correspondence, we calculate the vacuum decay rate for the Schwinger effect in confining large $N_{c}$ gauge theories. The instability is induced by the quark antiquark pair creation triggered by strong electromagnetic fields. The decay rate is obtained as the imaginary part of the Euler-Heisenberg effective Lagrangian evaluated from the D-brane action with a constant electromagnetic field in holographic QCD models such as the Sakai-Sugimoto model and the deformed Sakai-Sugimoto model. The decay rate is found to increase with the magnetic field parallel to the electric field, while it decreases with the magnetic field perpendicular to the electric field. We discuss generic features of a critical electric field as a function of the magnetic field and the QCD string tension in the Sakai-Sugimoto model.
Highlights
Within the AdS/CFT framework, the quark pair creation rate in the strongly coupled N = 4 supersymmetric Yang-Mills theory was obtained in [6, 7]
The decay rate is found to increase with the magnetic field parallel to the electric field, while it decreases with the magnetic field perpendicular to the electric field
We study the quark antiquark pair creation in non-supersymmetric QCD at large Nc at strong coupling, and the imaginary part of D8-brane action in a constant electromagnetic field
Summary
We derive an expression for the critical electric field Ecr in generic holographic QCD beyond which the Euler-Heisenberg Lagrangian acquires an imaginary part in the presence of a magnetic field. Which states that the critical electric field coincides with the confining force (the QCD string tension) σstring between a quark and an antiquark. It is a phase transition to a non-equilibrium steady state, and naively the critical electric field is expected to be equal to the confining force, that is, the QCD string tension. It is intriguing that our generic formula derived from string theory with the DBI action coincides with the QED expectation at strong magnetic field
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