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" "Supergravity theories generically contain non-compact global symmetry groups. The general rule is that the scalar fields of the theory in question parametrize a symmetric space. Thus, if the non-compact symmetry group is G, and its maximal compact subgroup is H, the scalar fields map the space-time into the symmetric space G/H, and the number of scalar fields is dim G – dim H. The first supergravity example of this type to be found, N = 4 supergravity is one of the most interesting. In this case there are two scalar fields and the symmetric space is SL(2,<math>R</math>)/SO(2).
John Henry Schwarz (born November 22, 1941) is an American theoretical physicist.
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String theory is an ambitious approach to the construction of a mathematical description of the physics that governs the properties of elementary particls and their interactions as well as the structure of space and time. It incorporates (and maybe even explains) well-established principles such as quantum mechanics and relativity. In fact, many string theorists (myself included) believe that string theory constitutes the third big physics revolution of the century, following relativity and quantum mechanics. It certainly requires conceptual advances every bit as bizarre and unexpected as was the case in the prior two revolutions.
Among the problems of the known string theories, as a theory of hadrons, was the fact that the spectrum of open strings contains massless spin 1 particles, and the spectrum of closed strings contains a massless spin 2 particle (as well as other massless particles), but there are no massless hadrons. In 1974, Joël Scherk and I decided to take string theory seriously as it stood, rather than forcing it to conform to our preconceptions. ... Specifically, Scherk and Schwarz (1974) proposed trying to interpret string theory as a unified quantum theory of all forces including gravity. Neveu and Scherk (1972) had shown that string theory incorporates the correct gauge invariances to ensure agreement at low energies (compared to the scale given by the string tension) with Yang-Mills theory. Yoneya (1973,1974) and Scherk and Schwarz (1974) showed that it also contains gauge invariances that ensure agreement at low energies with general relativity.
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One of the facts of nature is that there is what's called parity violation, which means that the fundamental laws are not invariant under mirror reflection. For example, a neutrino always spins clockwise and not counterclockwise, so it would look wrong viewed in a mirror. When you try to write down a fundamental theory with parity violation, mathematical inconsistencies often arise when you take account of quantum effects. This is referred to as the anomaly problem. It appeared that one couldn't make a theory based on strings without encountering these anomalies, which, if that were the case, would mean strings couldn't give a realistic theory. Green and I discovered that these anomalies cancel one another in very special situations. When we released our results in 1984, the field exploded. That's when Edward Witten [a theoretical physicist at the Institute for Advanced Study in Princeton], probably the most influential theoretical physicist in the world, got interested. Witten and three collaborators wrote a paper early in 1985 making a particular proposal for what to do with the six extra dimensions, the ones other than the four for space and time. That proposal looked, at the time, as if it could give a theory that is quite realistic. These developments, together with the discovery of another version of superstring theory, constituted the first superstring revolution.