The heat kernel expansion is a very convenient tool for studying one-loop divergences,
anomalies and various asymptotics of the effective action. The aim of this report is to collect …

We review what is known about boundary conditions in General Relativity on a spacetime of
Euclidean signature. The obvious Dirichlet boundary condition, in which one specifies the …

A bstract We generalize the\(T\overline {T}\) deformation of CFT 2 to higher-dimensional
large-N CFTs, and show that in holographic theories, the resulting effective field theory …

The literature on the spectral analysis of second order elliptic differential operators contains
a great deal of information on the spectral functions for explicitly known spectra. The same is …

We present the universal one-loop effective action up to dimension eight after integrating out
heavy fermion (s) using the Heat-Kernel method. We have discussed how the Dirac operator …

We describe a simple gauge-fixing that leads to a construction of a quantum Hilbert space
for quantum gravity in an asymptotically Anti de Sitter spacetime, valid to all orders of …

This book gives a detailed and self-contained introduction into the theory of spectral
functions, with an emphasis on their applications to quantum field theory. All methods are …

A bstract A well-defined variational principle for gravitational actions typically requires to
cancel boundary terms produced by the variation of the bulk action with a suitable set of …

A bstract We consider four-dimensional Euclidean gravity in a finite cavity. Dirichlet
conditions do not yield a well-posed elliptic system, and Anderson has suggested boundary …

The methods of the renormalization group and the ϵ-expansion are applied to quantum
gravity revealing the existence of an asymptotically safe fixed point in spacetime dimensions …