Schwinger pair production in hot anti–de Sitter space

We consider particle production in $1+1$ dimensional thermal anti–de Sitter space under the influence of a constant electric field. The vacuum-persistence amplitude is given by a nonrelativistic tunneling instanton once we interpret the system as being governed by an “equivalent” nonrelativistic Schrödinger equation. Working in the Wentzel–Kramers–Brillouin approximation, we calculate the tunneling rate in anti–de Sitter space at finite temperature and observe that the particle production rate is enhanced. Additionally, it is observed that there is a critical temperature beyond which the production rate is affected by the thermal environment. We claim this to be a new result for anti–de Sitter space in the semiclassical approximation.

Figure 1

The tunneling potentials for the (scalar) electron and positron in flat spacetime at zero temperature (left) and finite temperature (right). We see that in the case of finite temperature, with $\omega \ne 0$, an asymmetry exists in the potential which shifts it away such that the point of nucleation ceases to be the point of symmetry.