In theoretical physics, the Hořava–Witten theory argues that the cancellation of anomalies guarantees that a supersymmetric gauge theory with the E8 gauge group propagates on a type of domain wall. This domain wall, a Hořava–Witten domain wall, behaves as a boundary of the eleven-dimensional spacetime in M-theory. Proposed by Petr Hořava and Edward Witten, the theory is important for various relations between M-theory and superstring theory.
Background
D = 11 supergravity, which is the low energy limit of M theory, compactified over the one-dimensional unit interval yields heterotic string theory and compactified over the one-dimensional sphere yields Type IIA supergravity.Hořava & Witten 95, S. 2 This means that for a ten-dimensional smooth manifold , D = 11 supergravity on is equivalent to heterotic string theory on and D = 11 supergravity on is equivalent to D = 10 Type IIA supergravity on .
Description
In Hořava–Witten theory, D = 11 supergravity or more generally M theory is compactified over the unit interval , expressed as orbifold . For that, does not act free on by complex conjugation with fixed points . Alternatively, using the representation , one can use the involution given by sign swap. (This is different from the more Common free antipodal action of on with .) Metrics, diffeomorphisms und gravitino modes on are then those on invariant under the action of .Hořava & Witten 95, S. 3
Using the two fixed points of the action, hence both endpoints of the unit interval, two ten-dimensional theories can be connected using an eleven-dimensional theory. Hořava–Witten theory in particular studies the consequence of this correspondence on the anomalies of these theories, in particular of a cancellation is possible. On an eleven-dimensional smooth manifold, there are no gravitational anomalies, but there are in orbifolds. Furthermore, its fixed points lead to additional massless modes.
Hořava–Witten theory in particular studies M theory on the orbifold with two separate compactifications, one over the circle and one over the unit interval: In the former case, M theory is equivalent to Type IIA theory on , which is T-dual to Type I supergravity on . In the latter case, M theory is equivalent to heterotic string theory on . A connection fails due to the different gauge groups of Type I string theory and of the eponymous heterotic string theory.Hořava & Witten 95, S. 7 Both can however be connected to heterotic string theory. Typ I supergravity is S-dual to heterotic string theory and under symmetry breaking reduces to heterotic string theory, which also holds for heterotic string theory.
Hořava-Witten theory more generally studies M theory in the orbifold with an eleven-dimensional smooth manifold with an action of with a ten-dimensional fixed points space.Hořava & Witten 96, p. 3 (Exactly this is the case for with the fixed points space .)
Literature
References
External links
Hořava-Witten theory on nLab