RESEARCH

The plethora of objects in string theories can be traced back to two basic roots: M2-branes and M5-branes, which live in 11 dimensional space-time, ruled by the so-called M-Theory. The problem is, M-Theory is not yet fully understood. Our access to 11 dimensions is currently restricted to what occurs at low energy; a limited domain that is described by supergravity. 11 dimensional supergravity, however, is not just a random truncation of M-theory. There is a special class of objects (those that preserve supersymmetry) which exist in low energy realms and yet 'survive the transition to high energies'. Such objects, if they exist in supergravity, are guaranteed to be present in M-Theory as well; by studying them, we can glean information about otherwise hidden corners of M-Theory. 

M-branes can preserve supersymmetry, becoming a part of the privileged and protected class, if - in the given conditions - they are able to mould themselves into shapes which require the least possible energy to maintain . Such shapes are described by mathematical constructions known as calibrations, and are characteristic of a given surrounding or 'background'.  The complete list of calibrations in geometric backgrounds has long been known.

But the story does not end here. Backgrounds do not have to be purely geometric, they can also be suffused with a field of charge. In these latter situations, the response of an object to the surrounding charge will also need to be accounted for and the energy minimizing configurations will, correspondingly, change. In less abstract terms, this is analogous to what happens when we hold a pin in mid air and then let go; gravity pulls it pin down, because  the energy of the pin is minimized when it lies on the ground. If, however, a magnet is placed at a height nearby, the pin will fly there instead. This is not because the pin no longer cares to minimize its energy, but instead because the competing influences of charge and mass have conspired to change or 're-calibrate' the minimum energy configuration.  

An M-brane is a massive object, so (according to Einstein's General Relativity) the mere act of placing one somewhere, even in perfectly empty space, distorts the surrounding geometry. Additionally, since an M-Brane carries charge, it also acts as a source for a charged field. This background is clearly not purely geometric, so the exhaustive list of calibrations that had been drawn up earlier no longer applies

My research has focused mainly on finding, and classifying, the calibrations in such spaces. Once we know the calibrations, we know the minimal energy configurations, or equivalently, what the supersymmetric objects in this background are, and what they look like.  A list of my papers can be found here