Abstract
At strong-coupling and weak-field limit, the scalar Schwinger effect is studied by the field-theoretical method of worldline instantons for dynamic fields of single-pulse and sinusoidal types. By examining the Wilson loop along the closed instanton path, corrections to the results obtained from weak-coupling approximations are discovered. They show that this part of contribution for production rate becomes dominant as Keldysh parameter increases, it makes the consideration at strong coupling turn out to be indispensable for dynamic fields. Moreover a breaking of weak-field condition similar to constant field also happens around the critical field, defined as a point of vacuum cascade. In order to make certain whether the vacuum cascade occurs beyond the weak-field condition, following Semenoff and Zarembo’s proposal, the Schwinger effects of dynamic fields are studied with an {mathcal {N}}=4 supersymmetric Yang–Mills theory in the Coulomb phase. With the help of the gauge/gravity duality, the vacuum decay rate is evaluated by the string action with instanton worldline as boundary, which is located on a probe D3–brane. The corresponding classical worldsheets are estimated by perturbing the integrable case of a constant field.
Highlights
The pair-production rate in the constant electric field had been pioneered by Sauter, Heisenberg and Euler [8,9], and the corresponding Effect was named after Schwinger [10], who did the calculation based on field-theoretical approaches, see e.g. [11,12] for a current review
They show that this part of contribution for production rate becomes dominant as Keldysh parameter increases, it makes the consideration at strong coupling turn out to be indispensable for dynamic fields
We first show by a field-theoretical approach, that besides the enhancement due to the dynamics of electric fields, a further contribution to the production rate arises from the Wilson loop, and it becomes dominant in production rate as Keldysh parameter increases
Summary
The pair-production rate in the constant electric field had been pioneered by Sauter, Heisenberg and Euler [8,9], and the corresponding Effect was named after Schwinger [10], who did the calculation based on field-theoretical approaches, see e.g. [11,12] for a current review. Inspired by the similar existence of critical value of electric field in string theory, it is of a possibility to clarify the vacuum cascade in the Coulomb phase beyond the weak-field condition with the help of gauge/gravity duality [7,16,17]. We first show by a field-theoretical approach, that besides the enhancement due to the dynamics of electric fields, a further contribution to the production rate arises from the Wilson loop, and it becomes dominant in production rate as Keldysh parameter increases Such a correction seems to diverge as Keldysh adiabaticity parameter γ → ∞ based on our estimated formula; and it leads to a contradiction to the weak-field condition, so that near the critical field, the method itself breaks down, and the prediction of a vacuum cascade becomes unclear. The classical solution of the corresponding string worldsheets are estimated by perturbing the solvable case of a constant external electric field
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