We discuss the computation of the quantum effective action of strongly interacting field theories using holographic duality and its use to determine quasiequilibrium parameters of first-order phase transitions relevant for gravitational wave production. A particularly simple holographic model is introduced, containing only the metric and a free massive scalar field. Despite the simplicity, the model contains a rich phase diagram, including first-order phase transitions at nonzero temperature, due to various multitrace deformations. We obtain the leading terms in the effective action from homogeneous black brane solutions in the gravity dual and linearized perturbations around them. We then employ the effective action to construct bubble and domain wall solutions in the field theory side and study their properties. In particular, we show how the scaling of the effective action with the effective number of degrees of freedom of the quantum field theory determines the corresponding scaling of gravitational wave parameters.

We conduct large scale numerical simulations of gravitational wave production at a first-order vacuum phase transition. We find a power law for the gravitational wave power spectrum at high wave number which falls off as k(-1.5) rather than the k(-1) produced by the envelope approximation. The peak of the power spectrum is shifted to slightly lower wave numbers from that of the envelope approximation. The envelope approximation reproduces our results for the peak power less well, agreeing only to within an order of magnitude. After the bubbles finish colliding, the scalar field oscillates around the true vacuum. An additional feature is produced in the UV of the gravitational wave power spectrum, and this continues to grow linearly until the end of our simulation. The additional feature peaks at a length scale close to the bubble wall thickness and is shown to have a negligible contribution to the energy in gravitational waves, providing the scalar field mass is much smaller than the Planck mass.

Magnetic monopoles may be produced by the Schwinger effect in the strong magnetic fields of peripheral heavy-ion collisions. We review the form of the electromagnetic fields in such collisions and calculate from first principles the cross section for monopole pair production. Using the worldline instanton method, we work to all orders in the magnetic charge, and hence are not hampered by the breakdown of perturbation theory. Our result depends on the spacetime inhomogeneity through a single dimensionless parameter, the Keldysh parameter, which is independent of collision energy for a given monopole mass. For realistic heavy-ion collisions, the computational cost of the calculation becomes prohibitive and the finite size of the monopoles needs to be taken into account, and therefore our current results are not applicable to them-we indicate methods of overcoming these limitations, to be addressed in further work. Nonetheless, our results show that the spacetime dependence enhances the production cross section and would therefore lead to stronger monopole mass bounds than in the constant-field case.