Gravitational Duals from Equations of State
This solves a challenging inverse problem in theoretical physics, enabling the derivation of gravitational duals from quantum field theory equations of state, though it is incremental as it applies an existing neural network method to a new domain.
The authors tackled the inverse problem of determining the gravitational theory from a prescribed equation of state in holography, using physics-informed neural networks, and successfully applied it to theories with various phase transitions.
Holography relates gravitational theories in five dimensions to four-dimensional quantum field theories in flat space. Under this map, the equation of state of the field theory is encoded in the black hole solutions of the gravitational theory. Solving the five-dimensional Einstein's equations to determine the equation of state is an algorithmic, direct problem. Determining the gravitational theory that gives rise to a prescribed equation of state is a much more challenging, inverse problem. We present a novel approach to solve this problem based on physics-informed neural networks. The resulting algorithm is not only data-driven but also informed by the physics of the Einstein's equations. We successfully apply it to theories with crossovers, first- and second-order phase transitions.