Electromagnetic instability and Schwinger effect in the Witten–Sakai–Sugimoto model with D0–D4 background

Using the Witten–Sakai–Sugimoto model in the D0–D4 background, we holographically compute the vacuum decay rate of the Schwinger effect in this model. Our calculation contains the influence of the D0-brane density which could be identified as the $$\theta $$θ angle or chiral potential in QCD. Under the strong electromagnetic fields, the instability appears due to the creation of quark–antiquark pairs and the associated decay rate can be obtained by evaluating the imaginary part of the effective Euler–Heisenberg action which is identified as the action of the probe brane with a constant electromagnetic field. In the bubble D0–D4 configuration, we find the decay rate decreases when the $$\theta $$θ angle increases since the vacuum becomes heavier in the present of the glue condensate in this system. And the decay rate matches to the result in the black D0–D4 configuration at zero temperature limit according to our calculations. In this sense, the Hawking–Page transition of this model could be consistently interpreted as the confined/deconfined phase transition. Additionally there is another instability from the D0-brane itself in this system and we suggest that this instability reflects to the vacuum decay triggered by the $$\theta $$θ angle as it is known in the $$\theta $$θ-dependent QCD.