Dimensional reduction to hypersurface of foliation

Understand

When the bulk spacetime has a foliation structure, the collective dynamics of the hypersurfaces should reveal certain aspects of the bulk physics.

• The procedure of reducing the bulk to a hypersurface, called ADM reduction, was implemented in \cite{Park:2013iqa} where the 4D Einstein-Hilbert action was reduced along the radial reduction.
• In this work, reduction along the angular directions is considered {with a main goal to firmly establish the method of dimensional reduction to a hypersurface of foliation.} We obtain a theory on a 2D plane (the $(t,r)$-plane) and observe that novel and elaborate boundary effects are crucial for the consistency of the reduction.
• The reduction leads to a 2D interacting quantum field theory.