Scattering amplitudes, black holes and leading singularities in cubic theories of gravity

We compute the semi-classical potential arising from a generic theory of cubic gravity, a higher derivative theory of spin-2 particles, in the framework of modern amplitude techniques. We show that there are several interesting aspects of the potential, including some non-dispersive terms that lead to black hole solutions (including quantum corrections) that agree with those derived in Einsteinian cubic gravity (ECG). We show that these non-dispersive terms could be obtained from theories that include the Gauss- Bonnet cubic invariant G3. In addition, we derive the one-loop scattering amplitudes using both unitarity cuts and via the leading singularity, showing that the classical effects of higher derivative gravity can be easily obtained directly from the leading singularity with far less computational cost

Aspects of amplitudes, gravity & complexity

In this thesis, we explore two aspects of modern theoretical physics: scattering amplitudes in gravitational theories and entanglement entropy & complexity in quantum field theory. In part one, we utilise modern scattering amplitude techniques to efficiently calculate the deflection angle of both light and gravity due to the presence of a massive body. We find this to be in complete agreement with the prediction by General relativity. We then construct the scattering amplitudes of massive gravitons to probe the so-called van Dam-Veltman-Zakharov (vDVZ) discontinuity in a purely on-shell manner, which we again find to be in agreement with the usual result. Additionally, we provide a clear physical picture as to the source of the discontinuity that is often obscured by the usual formulation. In part two, we compare three different measures of complexity for a free bosonic QFT: circuit complexity, Fubini-Study complexity, and complexity from the covariance matrix. We show that circuit complexity is the most sensitive of the three, being the only measure able to distinguish between particular physically distinct time-evolved states. Finally, we compute the entanglement entropy, entanglement spectrum, and complexity for various phases of a topological insulator (described in this case by the Su-Schrieffer-Heeger (SSH) model), showing which physical features of the system each quantity captures as it transitions between conformal, topological and massive phases. We show that under certain circumstances, the complexity saturates later than the entanglement entropy, which contradicts the expectation from back hole interiors and AdS/CFT

Why is the Weyl double copy local in position space?

The double copy relates momentum-space scattering amplitudes in gauge and gravity theories. It has also been extended to classical solutions, where in some cases an exact double copy can be formulated directly in terms of products of fields in position space. This is seemingly at odds with the momentum-space origins of the double copy, and the question of why exact double copies are possible in position space and when this form will break has remained largely unanswered. In this paper, we provide an answer to this question, using a recently developed twistorial formulation of the double copy. We show that for certain vacuum type-D solutions, the momentum-space, twistor-space and position-space double copies amount to the same thing, and are directly related by integral transforms. Locality in position space is ultimately a consequence of the very special form of momentum-space three-point amplitudes, and we thus confirm suspicions that local position-space double copies are possible only for highly algebraically-special spacetimes.Comment: 23 pages plus references, 5 figure