# D8 branes in M-theory

The following table gives us the correspondence between objects in Type IIA Superstring theory and M-theory:

The D6 brane is magnetically dual to the D (10-6-4) = D0 brane and so magnetically couples to the RR gauge field $$A_{\mu}$$. My question is: what about the D8 brane from IIA superstring theory? What does it correspond to in M-theory?

The short answer is that it is not exactly known. Strictly speaking $$D8$$ branes appear in massive type IIA supergravity. Their precise lift to M-theory is not known, as far as my ignorance can tell.

Contrary to what is seems, the physics of $$D8$$ branes and $$O8$$ planes is delightfully beautiful, it offers wonderful counterexamples to common misconceptions and builds a bridge between math and exciting physics.

Some examples:

1. Stable does not imply BPS in string theory. See SO(32) Spinors of Type I and Other Solitons on Brane-Antibrane Pair to understand the statement in a basic context and Orientifold Precis for amusing counterexamples based on D8 branes.

2. $$D8$$ branes are generic examples that produce non trivial algebraic K-theory over the spacetime of which they are defects. On the Algebraic K-theory of The Massive D8 and M9 Branes is a very nice and clear reference on this.

3. $$D0$$ branes proving $$D8$$/anti-$$D8$$ pairs (with a suitable $$B$$-field turned on) compute the analogue of Donaldson-Thomas invariants for Calabi-Yau fourfolds. Magnificent Four

4. $$D8$$ branes can be used to separate different vacuas of string theory at finite spacetime distances! See my answer to Does different “side” of D-branes matter? for an example involving ten-dimensional type IIA and IIB theories separated at finite distance.

5. Spherical eight-branes are bubbles which form boundaries between different phases of the massive Type IIA supergravity theory. See Dynamic D8-branes in IIA string theory

Now I give another example by lifting $$D8$$ branes to M-theory:

There is a way to locally produce $$D8$$ branes in the type IIA theory in the presence of orientifold planes.

Here is the way: Compactify type I on circle, then apply a $$T$$-duality over it. The generic configuration of the compactification after $$T$$-duality contain 16 $$U(1)^{16}$$ (the maximal torus of $$Spin(32)/\mathbb{Z}_{2}$$) Wilson lines around the compact direction, among two orientifold $$O8$$ planes, each one with -16 units of RR-charge.

Recall that each Wilson line specify the position of a $$D8$$ brane at the circle and notice that in between two $$D8$$ branes the physics is locally the one given by type IIA superstring theory. The question is: how this last configuration lifts to M-Theory? Indeed, globally the construction lifts to heterotic M-theory (the strong coupling limit of the $$E_{8} \times E_{8}$$ heterotic string) with $$O8$$ planes lifting to the Horava-Witten domain walls and $$D8$$ branes lifting to stable non-BPS domain walls. Here is the amazement: The physics between any two of those domain walls is locally the same as the one of the M-theory, but the physics between a domain wall and the Horava-Witten wall is the one of the heterotic string (coupled to some new current algebras coming from the D8 lifts).

Aside comment: $$D8$$ branes are quite exotic. I recommend my answer to this question for another interesting example of such "exoticness" and why the the side of a $$D$$ brane at which you are actually matters.

References: