## Friday, January 06, 2006

### Ghost D-branes

Tadashi and Takuya have an interesting proposal to interpret the "fermionic" Chan-Paton factors - those that extend a gauge group from U(N) to a supergroup U(N/M) - as creating "ghost D-branes". All their states violate the spin-statistics relation. Note that the cancellation between these two D-branes may be viewed as perfect in topological string theory but Tadashi and Takuya talk about the full string theory.

When a D-brane coincides with a ghost D-brane, the configuration is equivalent to the closed string vacuum. However, when they are separated, they get a new configuration. Using these rules, I am a bit surprised that you can separate them. If the coincident D-brane and ghost D-brane contain no physical open string excitations, does not it mean that we should not be allowed to give one of them a vev?

They also discuss the heterotic dual. In this case, they extend the fermionic formulation by adding new chiral bosons to the 32 fermions.

#### 1 comment:

1. Ghost D-brane is an object that cancels the effects of an ordinary D-brane. A similar idea can clearly be applied to define ghost M2 and M5-branes in M-theory.

Ghost D-branes replace ordinary Chan-Paton matrices with supermatrices. The supergroups U(N|M) and OSp(N|M) arise as gauge symmetries in the supersymmetric world-volume theory of D-branes and ghost D-branes. This leads to a new type I string theory with gauge group OSp(32 + 2n|2n), type IIB string with gauge group U(n|n) (generalization of the type I/heterotic S-duality by including n ghost D9-branes on the type I side and by considering the heterotic string whose gauge group is OSp(32+2n|2n) and of the type IIB S-duality applied to D9- and ghost D9-branes with gauge group U(n|n)) and supergroup extension of the E8 × E8 heterotic string is E(8+n/2,n/2) × E(8+n/2,n/2) (which has infinitely many massless gauge fields) with any positive integer n. (This fact seems to be consistent with the known mathematical fact: there is no finite dimensional Lie superalgebra which is a counterpart for the En Lie algebra.)

A system with a pair of D-brane and ghost D-brane located at the same location is physically equivalent to the closed string vacuum. When they are separated, the system becomes a new brane configuration.

I suppose that matrix-valued tachyon on the worldline of a collection of n D0-brane and ghost D0-brane represents U-dual root lattice.