Agravity up to infinite energy.

The self-interactions of the conformal mode of the graviton are controlled, in dimensionless gravity theories (agravity), by a coupling that is not asymptotically free. We show that, nevertheless, agravity can be a complete theory valid up to infinite energy. When grows to large values, the conformal mode of the graviton decouples from the rest of the theory and does not hit any Landau pole provided that scalars are asymptotically conformally coupled and all other couplings approach fixed points.

New infra-red enhancements in 4-derivative gravity.

4-Derivative gravity provides a renormalizable theory of quantum gravity at the price of introducing a physical ghost, which could admit a sensible positive-energy quantization. To understand its physics, we compute ghost-mediated scatterings among matter particles at tree-level, finding a new power-like infra-red enhancement typical of 4-derivative theories, that we dub 'ghostrahlung'. Super-Planckian scatterings get downgraded to Planckian by radiating hard gravitons and ghosts, which are weakly coupled and carry away the energy.

Quantum mechanics of 4-derivative theories.

A renormalizable theory of gravity is obtained if the dimension-less 4-derivative kinetic term of the graviton, which classically suffers from negative unbounded energy, admits a sensible quantization. We find that a 4-derivative degree of freedom involves a canonical coordinate with unusual time-inversion parity, and that a correspondingly unusual representation must be employed for the relative quantum operator. The resulting theory has positive energy eigenvalues, normalizable wavefunctions, unitary evolution in a negative-norm configuration space.

Flux periodicities and quantum hair on holographic superconductors.

Superconductors in a cylindrical geometry respond periodically to a cylinder-threading magnetic flux, with the period changing from hc/2e to hc/e depending on whether the Aharonov-Bohm effects are suppressed. We show that holographic superconductors present a similar phenomenon, and that the different periodicities follow from classical no-hair theorems. We also give the Ginzburg-Landau description of the period-doubling phenomenon.