## Tuesday, February 27, 2007

### Matrix theory in 9 dimensions

I recommend you a new paper by
about the Matrix theory description of vacua with nine (8+1) flat infinite directions and 16 supercharges. The matrix model is generically a gauge theory on a cylinder. The only case in which it's that simple is the vacuum where the gauge group is broken down to SO(16) x SO(16) by a Wilson line around a circle in N=1, d=10 SUGRA-SYM coupled system - something that you can get both from the SO(32) and E8 x E8 starting points.

Recall that in 10D, the only really simple vacua with a matrix model description were type IIA with 32 supercharges and heterotic string theory with the E8 x E8 gauge group broken to SO(16) x SO(16) by longitudinal Wilson lines with 16 supercharges.

The other points of the moduli space they try to cover involve matrix models (2+1-dimensional generalized gauge theories) where the gauge coupling diverges as you approach one of the boundaries of the cylinder; they confirm the Kabat-Rey construction using a different interpretation. They have also (for the first time) looked at the description of the compactifications of M-theory on the Klein bottle and the Möbius strip, too - which also includes the Dabholkar-Park type IIA background with two different kinds of orientifolds (a perturbative dual of the Klein bottle compactification of M-theory) and the CHL string (the perturbative heterotic limit of the Möbius strip compactification of M-theory, with the exceptional group at level two).

Normally, orientifold O8-planes may coincide with D8-branes. You can keep on removing the D8-branes from the O8-plane, until the number of D8-branes is zero. That's what you would think except that they argue that you can actually remove one more, so that the number of remaining D8-branes on the O8-plane equals minus one. ;-) This O8-plane "in debt" must be infinitely strongly coupled but it still preserves the same supersymmetries. This novel discussion emerges from their unified description of the unoriented compactifications.