A Kind Of Magic

The road from Dunsink to the exceptional symmetries of M-theory

By Leron Borsten and Alessio Marrani 

Our journey starts in the fall of 1843 at the Dunsink Observatory[1], presiding from its hill-top vantage over the westerly reaches of Dublin City, seat to the then Astronomer Royal Sir William Rowan Hamilton. In the preceding months Hamilton had become preoccupied by the observation that multiplication by a complex phase induces a rotation in the Argand plane, revealing an intimate link between two-dimensional Euclidean geometry and the complex numbers ℂ. Fascinated by this unification of geometry and algebra, Hamilton set about the task of constructing a new number system that would do for three dimensions what the complexes did for two. After a series of trying failures, on October 16th 1843, while walking from the Dunsink Observatory to a meeting of the Royal Irish Academy on Dawson Street, Hamilton surmounted his apparent impasse in a moment of inspired clarity: rotations in three dimensions require a four-dimensional algebra with one real and three imaginary units satisfying the fundamental relations i= j= k= ijk = -1. The quaternions ℍ were thus born. Taken in that instant of epiphany, Hamilton etched his now famous equations onto the underside of Broome bridge, a cave painting illuminated not by campfire, but mathematical insight and imagination.  Like all great mathematical expressions, once seen they hang elegant and timeless, eternal patterns in the fixed stars merely chanced upon by our ancestral explorers.


Leron Borsten (left) and Alessio Marrani (right) stood before Hamilton’s fundamental relations, Broome bridge Dublin. Leron is currently a Schrödinger Fellow in the School of Theoretical Physics, Dublin Institute for Advanced Studies. Alessio is currently a Senior Grantee at the Enrico Fermi Research Centre, Roma.

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A brief history of Supergravity: the first 3 weeks


Stanley Deser is emeritus Ancell Professor of Physics at Brandeis University and a Senior Research Associate at Caltech

Prior to Supergravity’s (SUGRA’s) inception, the ideas in the air came from two new, quite different realms.  One realm was supersymmetry (SUSY); the other arose from the emerging difficulties in achieving consistent interactions between gravity and higher (s > 1) spin gauge fields.

Indeed, the Western discoverers of SUSY, Julius Wess and Bruno Zumino [1], would frequently visit Boston from NYU to spread the SUSY gospel, which did get even our blasé attention after a while, especially since the simplest SUSY multiplet pattern (s; s + 1/2) linking adjoining Fermi-Bose fields had no obvious reason to stop at the s = 0 and s = 1/2 models that had been studied thus far.
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