Mikołaj Korzyński, Julius Serbenta

We present an inequality between two types of distance measures to a single source in general relativity. It states that for a given emitter and observer the distance between them measured by the trigonometric parallax is never shorter than the angular diameter distance provided that the null energy condition holds and that there are no focal points in between. This result is independent of the details of the spacetime geometry or the motions of the observer and the source. The proof is based on the geodesic bilocal operator formalism together with well known properties of infinitesimal light ray bundles. Observation of the violation of the distance inequality would mean that on large scales either the null energy condition does not hold or that light does not travel along null geodesics.

James Bonifacio

The eigenvalues of the Laplace-Beltrami operator and the integrals of products of eigenfunctions and holomorphic $s$-differentials satisfy certain consistency conditions on closed hyperbolic surfaces. These consistency conditions can be derived by using spectral decompositions to write quadruple overlap integrals in terms of triple overlap integrals in different ways. We show how to efficiently construct these consistency conditions and use them to derive upper bounds on eigenvalues, following the approach of the conformal bootstrap. As an example of such a bootstrap bound, we find a numerical upper bound on the spectral gap of closed orientable hyperbolic surfaces that is nearly saturated by the Bolza surface.

Henriette Elvang, Matthew Dominique Mitchell

We use on-shell amplitude methods to systematically analyze the possibility of extended supersymmetry for 4d Galileon models, expanding on previous $\mathcal{N}=1$ results. Assuming spins $\le 1$, we prove that there exists no $\mathcal{N}=4$ supersymmetric extension of any 4d Galileons. Thus the Galileons cannot be part of the effective action of a single flat maximally supersymmetric D3-brane, and that explains why such terms do not appear in the $\alpha'$-expansion of the abelian open superstring amplitude. For $\mathcal{N}=2$ Galileons, we show that the complex scalar $Z = \phi + i \chi$ of the vector supermultiplet cannot have $\phi$ and $\chi$ both enjoy enhanced shift symmetry; instead, $\chi$ can at best be an $R$-axion with constant shift symmetry. Using the soft bootstrap, we demonstrate that the quartic DBI-Galileon is incompatible with $\mathcal{N}=2$ supersymmetry. A similar analysis performed at 7-point shows that a 2-parameter family of $\mathcal{N}=2$ supersymmetric quintic Galileons coupled with DBI passes the soft bootstrap. Finally, we show how supersymmetric coup\-lings between Galileons and gravitons arise in generalizations of our constructions, and we conclude with a discussion of Galileons and DBI-Galileons in the context of UV-completability vs.~the Swampland.