“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,R)/SO(2).”

p. 1

Adopted from Wikiquote. Last update June 3, 2021. History

Help us to complete the source, original and additional information

Do you have more details about the quote "Supergravity theories generically contain non-compact global symmetry groups. The general rule is that the scalar field…" by John Henry Schwarz?
John Henry Schwarz photo
John Henry Schwarz 5
American theoretical physicist 1941

Related quotes

Deane Montgomery photo

“THEOREM: if G is a locally euclidean, connected, simply connected topological group of dimension n greater than one, then G contains a closed proper subgroup of positive dimension.”

Deane Montgomery (1909–1992) American mathematician

[A theorem on locally euclidean groups, Annals of Mathematics, 1947, 650–658, 10.2307/1969132]

Sean Carroll photo

“Inflation is a simple idea: imagine that the universe begins in a tiny patch of space dominated by the potential energy of some scalar field, a kind of super-dense dark energy. This causes that patch to expand at a terrifically accelerated rate, smoothing out the density and diluting away any unwanted relics. Eventually the scalar field decays into ordinary matter and radiation, reheating the universe into a conventional Big Bang state, after which things proceed as normal.”

Sean Carroll (1966) American theoretical cosmologist

[The Eternally Existing, Self-reproducing, Frequently Puzzling Inflationary Universe, Preposterous Universe blog, 21 October 2011, http://www.preposterousuniverse.com/blog/2011/10/21/the-eternally-existing-self-reproducing-frequently-puzzling-inflationary-universe/]

Larry Wall photo

“Remember though thatTHERE IS NO GENERAL RULE FOR CONVERTING A LIST INTO A SCALAR.”

Larry Wall (1954) American computer programmer and author, creator of Perl

In the perl man page.
Documentation

“Sociometric space, e. g., the rating on a scale of leadership ability of each member of a group by every other member.”

James Grier Miller (1916–2002) biologist

Living Systems: Basic Concepts (1969)

Shiraz Minwalla photo

“With the string calculations to guide you can then correct these predictions. The corrected general expectations then apply to all quantum field theories, not just those very symmetric ones that string theory is able to analyse in detail.”

Shiraz Minwalla (1972) Indian physicist

Interview in The Hindu (2013)
Context: The improved understanding of the equations of hydrodynamics is general in nature; it applies to all quantum field theories, including those like quantum chromodynamics that are of interest to real world experiments. I think this is a good (though minor) example of the impact of string theory on experiments. At our current stage of understanding of string theory, we can effectively do calculations only in particularly simple — particularly symmetric — theories. But we are able to analyse these theories very completely; do the calculations completely correctly. We can then use these calculations to test various general predictions about the behaviour of all quantum field theories. These expectations sometimes turn out to be incorrect. With the string calculations to guide you can then correct these predictions. The corrected general expectations then apply to all quantum field theories, not just those very symmetric ones that string theory is able to analyse in detail.

David Gross photo
George Holmes Howison photo

“Mathematics is the science of the functional laws and transformations which enable us to convert figured extension and rated motion into number.—Howison, G. H.”

George Holmes Howison (1834–1916) American philosopher

"The Departments of Mathematics, and their Mutual Relations," Journal of Speculative Philosophy, Vol. 5, p. 170. Reported in Moritz (1914)
Journals

Lee Smolin photo

“The suggestion was that a positive energy proof for general relativity could be gotten by restricting supergravity to its bosonic sector, which is general relativity.”

Lee Smolin (1955) American cosmologist

"Positive energy in quantum gravity" arXiv (Jun 10, 2014)

Robbert Dijkgraaf photo

“Mirror symmetry is concerned with counting the number of holomorphic curves on Calabi-Yau manifolds, i.e. compact Kähler manifolds X with trivial canonical bundle KX.”

Robbert Dijkgraaf (1960) Dutch mathematical physicist and string theorist

[Mirror symmetry and elliptic curves by Robert Dijkgraaf, The moduli space of curves, 149–163, Progress in Mathematics, vol. 129, Birkhäuser Boston, 1995, 10.1007/978-1-4612-4264-2_5]

Gerald James Whitrow photo

“In 1922, Friedmann… broke new ground by investigating non-static solutions to Einstein's field equations, in which the radius of curvature of space varies with time. This Possibility had already been envisaged, in a general sense, by Clifford in the eighties.”

Gerald James Whitrow (1912–2000) British mathematician

The Structure of the Universe: An Introduction to Cosmology (1949)
Context: The models of Einstein and de Sitter are static solutions of Einstein's modified gravitational equations for a world-wide homogeneous system. They both involve a positive cosmological constant λ, determining the curvature of space. If this constant is zero, we obtain a third model in classical infinite Euclidean space. This model is empty, the space-time being that of Special Relativity.
It has been shown that these are the only possible static world models based on Einstein's theory. In 1922, Friedmann... broke new ground by investigating non-static solutions to Einstein's field equations, in which the radius of curvature of space varies with time. This Possibility had already been envisaged, in a general sense, by Clifford in the eighties.<!--p.82

Related topics