Monday, November 26, 2007
One of the recent jewels to arrive in hep-th is Paul Cook's Connections between Kac-Moody algebras and M-theory. This paper is actually a PhD thesis, under the supervision Peter West, the author of the well-known Introduction to Supersymmetry and Supergravity text.
By now, most people on the blogosphere have heard of the 248-dimensional Lie group E8. However, E8 isn't really "big" enough for M-theory. To capture the robust objects found in M-theory Cook argues one must use E8's Kac-Moody brother E11, i.e., that the Kac-Moody algebra E11 encodes the symmetries of M-theory.
As evidence for his conjecture, Cook finds the closure of a group G11 (an enlargement of the affine group IGL(11)) which includes two generators whose associated gauge fields are those of the only branes found in M-theory: the M2 and M5 branes. This essentially leads to a nonlinear realization of 11D-supergravity, where it is argued that a hidden E8 symmetry is manifest before the usual compactification to the three dimensions.
Friday, November 16, 2007
Garret Lisi's "Exceptionally Simple Theory of Everything" has been all the rage lately, being a hot topic of discussion at all the major physics blogs and even landing a front page article at New Scientist. Garrett's theory uses a non-compact form of E8, which supergravity buffs might recognize as a quasiconformal group for extremal black holes in homogeneous supergraviy. For the non-supergravity buffs this means the non-compact forms of E8 act as symmetry groups of the 57-dimensional charge-entropy space of microscopic black holes. This is the same 57-dimensional object mentioned in the E8 computation earlier this year.
From a quick listen of Garrett's talk at LSU, it seems the loop quantum gravity community finds Garrett's ideas to be promising. In the audio version of the talk, Smolin and Ashtekar can be heard commenting on a possible spin-network version of Garrett's model. Only time will tell if there is a spin-network/spin-foam formulation of Garrett's model. I, on the other hand, see more similarities with supergravity; and if this relation is real, there might actually be a topological string theory behind Garrett's TOE. D'oh! ;)