Abstract
Abstract We discuss some aspects of critical electric and magnetic fields in a field theory with holographic dual description. We extend the analysis of [1], which finds a critical electric field at which the Schwinger pair production barrier drops to zero, to the case of magnetic fields. We first find that, unlike ordinary weakly coupled theories, the magnetic field is not subject to any perturbative instability originating from the presence of a tachyonic ground state in the W-boson spectrum. This follows from the large value of the ’t Hooft coupling λ, which prevents the Zeeman interaction term to overcome the particle mass at high B. Consequently, we study the next possible B-field instability, i.e. monopole pair production, which is the S-dual version of the Schwinger effect. Also in this case a critical magnetic field is expected when the tunneling barrier drops to zero. These Schwinger-type criticalities are the holographic duals, in the bulk, to the fields E or B reaching the tension of F1 or D1 strings respectively. We then discuss how this effect is modified when electric and magnetic fields are present simultaneously and dyonic states in the spectrum can be pair produced by a generic E − B background. Finally, we analyze finite temperature effects on Schwinger criticalities, i.e. in the AdS-Schwarzshild black hole background.
Highlights
JHEP01(2013)174 will determine the behavior of the system in the presence of the electromagnetic fields
We extend the analysis of [1], which finds a critical electric field at which the Schwinger pair production barrier drops to zero, to the case of magnetic fields
With electric charges that sit at the extremities of the open string, there is a critical electric field at which a phase transition occurs
Summary
Where hab = diag(−L2r2, L2/r2) is the embedded worldsheet metric This has to be equal to the gauge theory mass mW = gv where v is the expectation value of the adjoint field and provides the relation between the bulk and boundary variables r0 and v given by v = 2lLs2√2rπ0gs (2.3). This gives the critical electric field as measured from the original coordinates (2.1): r02L2 ls2 This is interpreted in [1] as the critical field in the dual theory where pair production barrier drops to zero. Note that this derivation is entirely local, just a rescaling with the appropriate redshift factors from the local inertial frame to the original one. The basic reason is that the Euclidean solution for the pair production is more and more localized near the brane as we reach the critical value
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