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SUMMARY:A Magic Pyramid of Supergravity Theories from Yang-Mills Squared
DTSTART;VALUE=DATE-TIME:20210308T170000Z
DTEND;VALUE=DATE-TIME:20210308T180000Z
DTSTAMP;VALUE=DATE-TIME:20220518T235722Z
UID:indico-contribution-59@events.perimeterinstitute.ca
DESCRIPTION:Speakers: Mia Hughes (Imperial College London)\n"I will begin
by reviewing the unified description of pure Super Yang-Mills (SYM) Theory
(consisting of just a gauge field and gaugino) in dimensions 3\, 4\, 6\,
and 10 over the four normed division algebras R\, C\, H\, and O. Dimension
ally reducing these initial theories into dimensions 3\, 4\, 5\, 6\, 7\, 8
\, 9\, 10 gives a plethora of SYM theories written over the division algeb
ras\, with a single master Lagrangian to rule them all. In particular\, in
D = 3 spacetime dimensions\, the SYM theories with N = 1\, 2\, 4\, and 8
supersymmetries enjoy a unified description over R\, C\, H\, and O\, respe
ctively. In each spacetime dimension\, maximally supersymmetric theories a
re written over the octonions.\n\nIn apparently completely different devel
opments\, a popular thread in attempts to understand the quantum theory of
gravity is the idea of "gravity as the square of Yang-Mills". The idea in
its most basic form is that a symmetric tensor (graviton) can be built fr
om the symmetric tensor product of two vectors (Yang-Mills fields)\, an id
ea which can be extended to obtain entire supergravity multiplets from ten
sor products of SYM multiplets. Having established a division-algebraic de
scription of Super Yang-Mills theories\, I will then demonstrate how tenso
ring these multiplets together results in supergravity theories valued ove
r tensor products of division algebras.\n\nIn D = 3\, there are 4 SYM theo
ries (N = 1\, 2\, 4\, 8 over R\, C\, H\, O) and so there are 4 x 4 = 16 po
ssible supergravity theories to obtain by "squaring Yang-Mills". The globa
l symmetries of these 16 division-algebraic SYM-squared supergravity theor
ies are precisely those belonging to the 4 x 4 Freudenthal-Rosenfeld-Tits
"magic square" of Lie algebras! Furthermore\, the scalar fields in these s
upergravity theories describe non-linear sigma models\, whose target space
manifolds are division algebraic projective planes! Performing the same t
ensoring of SYM theories in spacetime dimensions D > 3 results in a whole
"magic pyramid" of supergravities\, with the magic square at the base in D
= 3 and Type II supergravity at the apex in D = 10. This construction giv
es an explicit octonionic explanation of many of the mysterious appearance
s of exceptional groups within string/M-theory and supergravity."\n\nhttps
://events.perimeterinstitute.ca/event/5/contributions/59/
LOCATION:
URL:https://events.perimeterinstitute.ca/event/5/contributions/59/
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