#### Alladi Ramakrishnan Hall

#### A New Path Integral for Quantum Gravity

#### Chethan Krishnan

##### IISc, Bangalore

*We introduce a boundary term for gravity that makes the Einstein-Hilbert action a well-defined variational problem for general Neumann boundary conditions. It is then used to define a (semi-classical) Euclidean path integral that correctly reproduces gravitational thermodynamics in asymptotically flat space. In asymptotically AdS spaces this gives rise to new counter-terms and a finite renormalized on-shell action. We will argue that the fluctuations that respect our boundary conditions are "normalizable" (when the boundary metric is dynamical and is controlled by the trace anomaly), suggesting that this could be a new definition for quantum gravity in AdS. Some preliminary comments will be made about formulating holography in terms of effective actions instead of generating functionals, which could be relevant for this.*

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