BMS Supertranslations and Not So Soft Gravitons

In a previous article, we have argued that Low's sub-leading soft photon theorem can be recovered as a Ward identity associated to the same large gauge transformations that control the leading piece of the theorem. The key for that was to link the energy expansion displayed in the soft theorem to a $\frac{1}{r}$ expansion that we can perform in the associated asymptotic charge. We expect this idea to be valid in general, and here we provide compelling evidence for it by showing how the same method works in the case of Einstein-Hilbert gravity. More precisely, we are able to derive the three orders of the tree-level soft graviton theorem simply from the BMS supertranslation charge, known to give rise to the leading soft graviton theorem. In particular, we do not need to invoke superrotations (nor extended superrotations) at any point of the argument.Comment: v2: 26 pages, moderate revision with corrections and clarifications, refs adde

Maximal rationally connected fibrations and movable curves

A well known result of Miyaoka asserts that a complex projective manifold is uniruled if its cotangent bundle restricted to a general complete intersection curve is not nef. Using the Harder-Narasimhan filtration of the tangent bundle, it can moreover be shown that the choice of such a curve gives rise to a rationally connected foliation of the manifold. In this note we show that, conversely, a movable curve can be found so that the maximal rationally connected fibration of the manifold may be recovered as a term of the associated Harder-Narasimhan filtration of the tangent bundle.Comment: An error in the argumentation has been correcte

Tangential projections and secant defective varieties

Going one step further in Zak's classification of Scorza varieties with secant defect equal to one, we characterize the Veronese embedding of $\P^n$ given by the complete linear system of quadrics and its smooth projections from a point as the only smooth irreducible complex and non-degenerate projective subvarieties of $\P^N$ that can be projected isomorphically into $\P^{2n}$ when $N\geq\binom{n+2}{2}-2$.Comment: To appear in Bulletin of the London Mathematical Societ

Holography and holomorphy in quantum field theories and gravity

This Ph.D. thesis deals with the application of complex analysis and holographic methods to study both the perturbative and the non-perturbative regimes of Quantum Field Theories and Gravity. Although Gravity does not admit a full quantum picture, its classical description is fine at tree level and it becomes useful for studying strongly coupled gauge theories through the gauge/gravity correspondence. We first study a generalization of the BCFW on-shell recursion relation, which allows us to characterize the tree-level scattering amplitudes of theories of massless particles in a fashion completely detached from the usual Feynman representation. This permits proposing a novel approach to the construction of theories which, despite being only valid at tree level and just for theories of massless particles, returns in a very simple manner some powerful facts, well-known from the traditional Lagrangian analysis. Then we focus on obtaining several new supergravity solutions dual to supersymmetric gauge theories with fundamental matter (flavor) in the Veneziano limit. These solutions must incorporate the backreaction of an infinite number of flavor branes. We choose to smear these branes in order to find analytical solutions. We find fully regular solutions describing the strongly coupled dynamics of flavor in the ABJM theory and in a SQCD-like theory. For the former, the solution has an AdS factor, and many checks can be done confirming that the supergravity solution is a faithful dual. For the latter, some checks can also be done, and more interestingly, phenomenological applications that might be relevant for Beyond-the-Standard-Model Physics can be found. Finally, we illustrate other uses of the gauge/gravity correspondence by finding supergravity solutions dual to theories exhibiting a Kutasov duality and SQCD-like theories in two and three dimensions