My current research centers around the geometry of supersymmetric supergravity backgrounds.
Supergravity theories arise naturally as the field-theory limit of string theories, and this fact is perhaps the major contributor to the interest in supergravity today.
Supergravity is a nontrivial extension of Einstein's theory of General Relativity. Supergravity theories are very rigid, their structure dictated by the representation theory of certain "kinematic" Lie superalgebras. Indeed, when this algebra is sufficiently big — "when there is enough supersymmetry" — the supergravity theory is actually unique.
Studying the possible classical supergravity backgrounds is one way to study the possible spacetime geometries on which strings can propagate consistently. Of course, supergravity is only a valid approximation to string theory in certain regimes. If the geometry begins to curve too much, stringy effects become relevant and much of the differential geometric flavour of the theory starts to fade.
At a purely geometric level, the study of supergravity backgrounds is the study of solutions of certain linear partial differential equations on spinor fields and of the geometries which admit them. Spinors satisfying these equations are called Killing spinors and solutions admitting Killing spinors are called supersymmetric.
In the immediate aftermath of the second superstring revolution of 1994-5, it became clear that much could be learnt about nonperturbative string theory by studying supersymmetric solutions to supergravity theories. I have since advocated a more systematic approach to the study of these backgrounds, and this is the path I have followed in my research.
This research has been funded in part by the EPSRC.
Debes amar la arcilla que va en tus manos
debes amar su arena hasta la locura
y si no, no la emprendas que será en vano
sólo el amor alumbra lo que perdura
sólo el amor convierte en milagro el barro.
Debes amar el tiempo de los intentos
debes amar la hora que nunca brilla
y si no, no pretendas tocar lo cierto
sólo el amor engendra la maravilla
sólo el amor consigue encender lo muerto.
— Silvio Rodríguez