Gravity: Supersymmetry

March 25, 2009, 8:39 pm
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While the quantum gravity program got hoplessly bogged-down in these and otherthorny issues, in 1973, a breakthrough occurred in another area of theoretical physics. Some might even call it a miracle.

In a pair of papers describing something called a 'supergauge transformation', Wess at Karlsruhe University, and Zumino at CERN presented some of the intricatemathematical work they had been doing for the last few years on a peculiar classof mathematical transformations. These transformations acted upon a set of 'superfields' they had defined, and led to inter-spin and half-integer spin particles changeing their hats.

Previously, the kinds of transformations theoreticians had worked with preserved the spin character of the fields they operated upon, but if you defined a new kind of a superfield as havinga mixture of integer and half-integer components, the superfield would remain unchanged while its sub-components changed reversed their roles.  The implications of the Wess-Zumino supersymmetry theory were revolutionary.

The fermionic and bosonic particles had to have masses that were strictly related to one another, and even more surprising, some of the pesky infinities that plagued the field theories of each of these components individually, went away because of the strictures imposed by the new supersymmetry. For supersymmetry to work, the basic fields in nature must be a set of superfields which have both fermion and boson components. The  structure of the superfield  is fixed so that only the following spins get paired together: [ spin-2 , spin 3/2 ], [spin 1, spin 1/2].. This means that forevery lepton and quark, there is paired with it a supersymmetry partner field with spin 1; for every graviton with spin-2, there is a spin 3/2 'gravitino' field. But when these new fields are added to the calculations of particle dynamics, they miraculously contribute their own infinities which are opposite to the ones contributed by the ordinary matter. The annoying infinities in some quantum gravity calculations are eliminated by the inclusion of the spin 3/2 superpartner fields. 

With supergravity theory, a calculation would be performed by converting the other fields into the [2,3/2] gravity superfamily, and then carrying out the calculation in terms of these spin-2, spin 3/2 field components. This would lead to a finite result, and you then transform the result backinto the original superfield components to get the answer you wanted for the process you were considering.  A curious feature of the supersymmetry transformation is that when it is performed twice on the same particle, the relationship between the field before and after was one of translation in spacetime. The particle moves from one location to another. Because gravity and spacetime are so intimately linked, this could only mean that buried somewhere inside the mystery of supersymmetry was the hint of a theory that included gravity.

By 1975, Ferrara and Zumino were able to show that supersymmetryimplied that a pair of super fields should exist one of which had a spin-2 and a spin 3/2 components paired together as a unit which they later cristened the gravitational supermultiplet. A few years later Stanly Deser, Bruno Zumino, Daniel Freedman and Peter van Nieuwenhuisen discovered something even more remarkable.

When the original 'global' supersymmetry was made into a 'local' supersymmetry, gravitational fields appeared. For several years afterwards,supersymmetry models were explored with increasing excitement until 1977 when Murray Gell-Mann, at a meeting of the Washington, D.C. American Physical Society, announced some rather troubling news. Even the largest supergravity theory known at that time, SO(8), didn't have enough fields in it to accomodate the known fields in nature. SO(8) had 1 graviton field, 8 spin 3/2 fields, 28 spin-1 fields, 56 spin 1/2 fields and 70 spin-0 fields. No one, by the way, had ever seen a spin-0 field, let alone 70 different kinds of them, and the 56 spin 1/2 fields did not match up with the known leptons and quarks. Could the Higgs fields that are also spin-0 particles be accomodated by SO(8) supergravity? The answer seemed to be 'No'. They would still be an extra set of fields above and beyond the 70 supersymmetric, spin-0 particles. Supersymmetry would also need to be a broken symmetry in our universe because none of the superpartner fields to the ordinary quarks, leptons and bosons have been observed at energies below 100 GeV.

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Odenwald, Sten, Ph.D. (Contributing Author); Bernard Haisch (Topic Editor). 2008. "Gravity: Supersymmetry." In: Encyclopedia of the Cosmos. Eds. Bernard Haisch and Joakim F. Lindblom (Redwood City, CA: Digital Universe Foundation). [First published February 13, 2008].




(2009). Gravity: Supersymmetry. Retrieved from


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