Abstract
Remembering the foundational contributions of Peter Freund to supergravity, and especially to the problems of dimensional compactification, reduction is considered with a non-compact space transverse to the lower dimensional theory. The known problem of a continuum of Kaluza–Klein states is avoided here by the occurrence of a mass gap between a single normalizable zero-eigenvalue transverse wavefunction and the edge of the transverse state continuum. This style of reduction does not yield a formally consistent truncation to the lower dimensional theory, so developing the lower-dimensional effective theory requires integrating out the Kaluza–Klein states lying above the mass gap.
Highlights
The fact that supergravity and superstring theories originate most naturally in higher spacetime dimensions – 11 for maximal supergravity and 10 for superstring theories – gave rise to intensive research on reduction schemes starting in the early 1980s
A key achievement was made in the 1980 paper by Peter Freund and Mark Rubin on the reduction via an S7 transverse geometry from D = 11 down to D = 4 spacetime dimensions [1]
The reduction mechanism involved turning on flux for the 4form antisymmetric-tensor field strength of the D = 11 theory, as well as a warped-product structure for the overall higher dimensional spacetime
Summary
The fact that supergravity and superstring theories originate most naturally in higher spacetime dimensions – 11 for maximal supergravity and 10 for superstring theories – gave rise to intensive research on reduction schemes starting in the early 1980s. A key achievement was made in the 1980 paper by Peter Freund and Mark Rubin on the reduction via an S7 transverse geometry from D = 11 down to D = 4 spacetime dimensions [1] In this highly influential paper, the “ground state” maximally symmetric geometry in D = 4 proved to be an Anti de Sitter space. The reduction mechanism involved turning on flux for the 4form antisymmetric-tensor field strength of the D = 11 theory, as well as a warped-product structure for the overall higher dimensional spacetime All of these features have remained prominent in the subsequent development of string and supergravity theories: the key roles of warped products, Anti de Sitter vacua and the importance of flux vacua. Another of Peter’s topics which intertwines with much of current research was the characterization of gauge fields as Nambu-Goldstone fields for the nonlinear realization of a higher symmetry [7]
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