SO(8) and G2 × G2 N = 1 Supergravities in
نویسندگان
چکیده
We construct the N = 1 supergravity analog of the Green-Schwarz and heterotic superstring theories in 10D. We find the SO(8) theory previously found by compactification of 10D on K3. We also find eleven G 2 × G 2 theories, two with symmetric matter content. It is not obvious how tenof the G 2 × G 2 theories can be gotten from 10D. Ten-dimensional superstrings [1], [2], [3], [4] are one of the most important discoveries of our time. They have led to fundamental advance in the way we perceive the relationships between particle physics, condensed matter physics, gravity and mathematics. The zero slope limit of the Green-Schwarz S0(32) open string theory in 10D is an N = 1 supergravity theory, and is interesting in its own right. The important observation [2] that the leading gauge anomaly[5] in SO(N) is proportional to (N − 32) means only SO(32) is possible. The development of the Green-Schwarz mechanism restored consistency to the theory, but only for S0(32) where in addition 496 gauge group generators (vector fields) are required to cancel the perturbative gravitational anomaly. Once the SO(32) open string theory and then the heterotic theory were established, much progress was made by various methods of compactification, and by investigating generalized solitons and instantons (p-branes, D-branes, etc.) and other nonperturbative aspects including dualities in these and related theories. By extending the theories to 11 and 12 dimensions in the so-called M and F theories relations were discovered among the 10D theories.
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