Holographic Schwinger effect in a rotating strongly coupled medium

An interesting phenomenon in quantum electrodynamics (QED) is pair production in a strong electric field, known as the Schwinger effect [1]. The production rate of charged particles, such as electrons and positrons, was first computed by Schwinger for weak-coupling and weak-fields [1] using

whereE,e, andmare the external electric field, elementary electric charge, and electron mass, respectively. There is no critical field in this scenario. Subsequently, Affleck et al. extended the calculation of Γ to the case of arbitrary-coupling and weak-fields [2],

for which there is a critical field at $ E_c = (4\pi/e^3)m^2\simeq 137m^2/e $ . However, this critical value does not satisfy the weak-field condition, that is, $ eE\ll m^2 $ . Therefore, it seems that $ E_c $ cannot be obtained under the weak-field condition. Furthermore, to verify the existence of $ E_c $ , one must work beyond the weak-field condition.

The Schwinger effect is not restricted to QED but a universal aspect of quantum field theories (QFTs) coupled to aU(1) gauge field. However, studying this effect in a QCD-like or confining theory using QFTs is difficult because the (original) Schwinger effect is non-perturbative. Fortunately, the AdS/CFT correspondence [3–5] provides an alternative approach. Semenoff and Zarembo pioneered the holographic Schwinger effect using this method and found [6]

whereλis the 't Hooft coupling constant, andmdenotes the mass of the fundamental scalar fields in theW-boson supermultiplet, for example,W-bosons or quarks. Interestingly, the critical value agrees with the Dirac-Born-Infeld (DBI) result [7]. Since then, there has been growing research interest in the holographic Schwinger effect in this direction [8–22] (for a recent review see [23]).

Here, we extend the study of the (holographic) Schwinger effect to a rotating medium using potential analysis. It has been argued that [24–28] the quark gluon plasma (QGP) produced in (typical) noncentral heavy-ion collisions may carry a nonzero angular momentum (related to colliding nuclei) of the order of $ 10^4 $ – $ 10^5\;\hbar $ with local angular velocity in the range of 0.01–0.1 GeV. Most of the angular momentum is removed by spectator nucleons, but some might remain in the medium [29–31]. Certainly, there is little hope of obtaining a significant correction owing to the angular velocity in current experiments; however, this may be observed in the near future. Moreover, AdS/CFT can be as insightful within this issue, and various observables and quantities have already been studied, such as drag force [32–34], the jet quenching parameter [35,36], energy loss [37–39], phase transition [40], and free energy [41]. Inspired by this, we investigate the effect of angular velocity on the Schwinger effect in a deformed AdS black-hole background. In particular, we study how angular velocity affects the production rate in this scenario. This study could be regarded as an extension of [8] with a confining scale and angular velocity.

This paper is structured as follows: In the next section, we briefly review the rotating background considered in this study. In section III, we perform potential analysis on the Schwinger effect in this background and analyze how angular velocity affects the production rate. Moreover, we determine the critical field from DBI action. Finally, the results and directions of future research are discussed in section IV.

Holographic QCD models, such as hard wall [42,43], soft wall [44,45], and improved holographic QCD [46–51], have achieved considerable success in describing various aspects of hadron physics. Here, we adopt a type of soft wall model [45],