D8 branes 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:

1. Some Properties of Type I' String Theory

2. On the M-theory Interpretation of Orientifold Planes

3. M theory and orientifolds

4. Orientifold point in M theory

5. "D8-brane" nlab entry