Scattering amplitudes computed at a fixed loop order, along with any other object computed in perturbative QFT, can be expressed as a linear combination of a finite basis of loop integrals. To compute loop amplitudes in practise, such a basis of integrals must be determined. In this talk I introduce a new algorithm for finding bases of loop integrals and discuss its implementation in the publically available package Azurite.

# Past Relativity Seminar

**I will discuss recent developments in the study of scattering amplitudes in Einstein-Yang-Mills theory. At tree level we find new structures at higher order collinear limits and novel connections with amplitudes in Yang-Mills theory using the CHY formalism. Finally I will comment on unitarity based observations regarding one-loop amplitudes in the theory. **

We consider two-dimensional chiral, first-order conformal field theories governing maps from the Riemann sphere to the projective light cone inside Minkowski space -- the natural setting for describing conformal field theories in two fewer dimensions. These theories have a SL(2) algebra of local bosonic constraints which can be supplemented by additional fermionic constraints depending on the matter content of the theory. By computing the BRST charge associated with gauge fixing these constraints, we find anomalies which vanish for specific target space dimensions. These critical dimensions coincide precisely with those for which (biadjoint) cubic scalar theory, gauge theory and gravity are classically conformally invariant. Furthermore, the BRST cohomology of each theory contains vertex operators for the full conformal multiplets of single field insertions in each of these space-time CFTs. We give a prescription for the computation of three-point functions, and compare our formalism with the scattering equations approach to on-shell amplitudes.

Superradiance in black hole spacetimes is a phenomenon by which a field of spin 0 or 1 can extract energy from the background. Typically, one can imagine sending a wave packet with a given energy towards a black hole and receiving in return a superposition of wave packets carrying a total amount of energy that is larger than the energy sent in. It can be caused by rotation or by interaction between the charges of the black hole and the field. In the first case, the region where superradiance takes place (the ergoregion) has a clear geometrical localization depending only on the physical parameters of the black hole. For charge induced superradiance, this is not the case and we have a generalized ergoregion depending also on the physical properties of the field (mass, charge, angular momentum). In the most severe cases, the generalized ergoregion may cover the whole exterior of the black hole. We focus on charge-induced superradiance for spin 0 fields in spherically symmetric situations. Alain Bachelot wrote a thorough theoretical study of this question in 2004, which, to my knowledge, is the only work of its kind. When I was in Bordeaux, he and I discussed the possibility of investigating superradiance numerically. Over the years it became an actual research project, involving Laurent Di Menza and more recently Mathieu Pellen, of which this talk is an account. The idea was to observe numerically some superradiant behaviours and gain a more precise understanding of the phenomenon. We shall show an exact analogue of the Penrose process with the superradiance of wave packets and a slightly different behaviour for fields "emerging" inside the ergoregion. We shall also explore the related question of black hole bombs and present some recent observations.

Shortly after Mason & Skinner introduced the so-called ambitwistor strings, Berkovits came up with a pure-spinor analogue of the theory, which was later shown to provide the supersymmetric version of the Cachazo-He-Yuan amplitudes. In the heterotic version, however, both models give somewhat unsatisfactory descriptions of the supergravity sector.

In this talk, I will show how the original pure-spinor version of the heterotic ambitwistor string can be modified in a consistent manner that renders the supergravity sector treatable. In addition to the massless states, the spectrum of the new model --- which we call sectorized heterotic string --- contains a single massive level. In the limit in which a dimensionful parameter is taken to infinity, these massive states become the unexpected massless states (e.g. a 3-form potential) first encountered by Mason & Skinner."

Any constant-scalar-curvature Kaehler (cscK) metric on a complex surface may be viewed as a solution of the Einstein-Maxwell equations, and this allows one to produce solutions of these equations on any 4-manifold that arises as a compact complex surface with even first Betti number. However, not all solutions of the Einstein-Maxwell equations on such manifolds arise in this way. In this lecture, I will describe a construction of new compact examples that are Hermitian, but not Kaehler.

Some recent applications of supertwistors to superparticle mechanics will be reviewed.

First: Supertwistors allow a simple quantization of the N-extended 4D massless superparticle, and peculiarities of massless 4D supermultiplets can then be explained by considering the quantum fate of a classical ``worldline CPT'' symmetry. For N=1 there is a global CPT anomaly, which explains why there is no CPT self-conjugate supermultiplet. For N=2 there is no anomaly but a Kramers degeneracy explains the doubling of states in the CPT self-conjugate hypermultiplet.

Second: the bi-supertwistor formulation of the N-extended massive superparticle in 3D, 4D and 6D makes manifest a ``hidden’’ 2N-extended supersymmetry. It also has a simple expression in terms of hermitian 2x2 matrices over the associative division algebras R,C,H.

Third: omission of the mass-shell constraint in this 3D,4D,6D bi-supertwistor action yields, as suggested by holography, the action for a supergraviton in 4D,5D,7D AdS. Application to the near horizon AdSxS geometries of the M2,D3 and M5 brane confirms that the graviton supermultiplet has 128+128 polarisation states.

Locality is not expected to be a fundamental aspect of a full theory of quantum gravity; it should be emergent in an appropriate semiclassical limit. In the context of general holography, I'll define a new construct - the causal state - which provides a necessary and sufficient condition for a boundary state to have a holographic semiclassical dual causal geometry (and thus be "local"). This definition illuminates some general features of holographic quantum gravity: for instance, I'll show that the emergence of locality is "all or nothing" in the sense that it exhibits features of quantum error correction and quantum secret sharing. In the special case of AdS/CFT, I'll also argue that the causal state is the natural boundary dual to the so-called causal wedge of a region.

This talk is about a 4d "(ambi-)twistor string" formula for sEYM tree-level scattering amplitudes and is work in progress. The formula sheds some new light on the translation between CHY formulae and (ambi-)twistor formulae in general, potentially even at loop level.

In this talk, I discuss the positive geometry of the Wilson Loop Diagrams appearing in SYM N-4 theory. In particular, I define an algorithm for associating Wilson Loop diagrams to convex cells of the positive Grassmannians. Using combinatorics of these cells, I then consider the geometry of N^2MHV diagrams on 6 points.