Existence of a 7-brane exchanging the two E8 factors

Construct or demonstrate the existence, within ten-dimensional E8×E8 heterotic string theory, of a non-BPS codimension-two 7-brane whose monodromy exchanges the two E8 gauge factors and whose tension can be made sufficiently small in some region of moduli space so that a macroscopic loop is not hidden behind its Schwarzschild horizon.

Background

The exchange of the two E8 factors is a Z2 symmetry of the ten-dimensional E8×E8 heterotic string. If realized as a monodromy around a codimension-two brane whose tension can be made small in some moduli regime, such a brane would provide a direct, observable manifestation that this Z2 is a discrete gauge symmetry via monodromy experiments. However, no explicit construction of such a brane is currently known.

Establishing the existence (or non-existence) of this 7-brane would clarify whether the E8 exchange symmetry admits a brane realization suitable for the proposed monodromy-based symmetry tests.