Holographic Schwinger effect in the confining background with D-instanton

Abstract

Using the gauge-gravity duality, we study the holographic Schwinger effect by performing the potential analysis on the confining D3- and D4-brane background with D-instantons then evaluate the pair production/decay rate by taking account into a fundamental string and a single flavor brane respectively. The two confining backgrounds with D-instantons are obtained from the black D(-1)–D3 and D0–D4 solution with a double Wick rotation. The total potential and pair production/decay rate in the Schwinger effect are calculated numerically by examining the NG action of a fundamental string and the DBI action of a single flavor brane all in the presence of an electric field. In both backgrounds our numerical calculation agrees with the critical electric field evaluated from the DBI action and shows the potential barrier is increased by the presence of the D-instantons, thus the production/decay rate is suppressed by the D-instantons. The interpretation is that particles in the dual field theory could acquire an effective mass through the Chern-Simons interaction or the theta term due to the presence of D-instantons so that the pair production/decay rate in Schwinger effect is suppressed since it behaves as $$e^{-m^{2}}$$ e - m 2 . This conclusion is in agreement with the previous results obtained in the deconfined D(-1)–D3 background at zero temperature limit and from the approach of the flavor brane in the D0–D4 background. In this sense, this work may be also remarkable to study the phase transition in Maxwell–Chern–Simons theory and observable effects by the theta angle in QCD.

Holographic Schwinger effect and electric instability with anisotropy

“…However the calculations in [1,2] imply Schwinger effect is non-perturbative, thus it is very challenging to evaluate Schwinger effect in the framework of quantum field theory (QFT) strictly. Fortunately, the gauge-gravity duality and AdS/CFT may provide an alternative method to study the strongly coupled QFT [9,10], in particular, to evaluate Schwinger effect in holography [11][12][13][14][15][16][17][18][19]. Since the equivalence between the type IIB super string theory on AdS 5 × S 5 and the four-dimensional N = 4 SU (N c ) super Yang-Mills theory on N c D3-branes is the most famous example in gauge-gravity duality, the authors of [20,21] construct the solution in type IIB supergravity then obtain anisotropic black brane solution and bubble solution as gravity soliton in order to study anisotropic gauge theory at finite temperature and with confinement respectively.…”

“…Note that in the bubble solution, the dual theory is defined at zero temperature limit since the period of t is infinity. And the bubble solution would be very useful to study the Schwinger effect in a confining system as [14,16,17,19]. A worthy notable feature here is that if we remain to employ the analytical formulas of F , B, φ in the bubble solution, it refers to the case that the size of the compactified direction z trends to be vanished so that the dual theory becomes exactly three-dimensional.…”

“…In this section, we will evaluate the pair production rate according to the AdS/CFT dictionary which is to compute the onshell action of a fundamental open string in bulk with circular trajectory of each endpoint in the boundary, as it is illustrated in figure 8. Since our concern is the radial dependence of string embedding, it would be convenient to choose the polar coordinates on the probe brane located at boundary as [12,16,18,19]. However this would be a little tricky due to the anisotropy in the background geometry.…”

“…Solving the constraint of E ,⊥ and u * in (5.17) (5.18), we plot out the behavior of ImL ,⊥ in (5. 19) as a function of E ,⊥ in figure 12 and 13.…”

The D4/D8 Model and Holographic QCD

“…while the other constants must be confirmed by imposing additional physical conditions. Nevertheless, one may find that the phase transition depends only on the integration constants given in (123).…”