Deconstructing the E₀ SCFT to Solve the Orbifold Paradox of the Heterotic M Theory

Many heterotic orbifold models have massless twisted-sector particles with simultaneous E8_1 and E8_2 charges. In the strong-coupling M-theory dual of the heterotic string this poses a paradox: Since the E8_1 and E8_2 live at opposite ends of the x^10 dimension, where could a massless particle with both types of charges possible live? To key to this question are the 5D SCFTs living at the orbifold fixed planes going through the bulk of the M theory. We use dimensional deconstruction to understand how such a 5D SCFT (specifically, the E_0 SCFT at the Z_3 fixed point) works at the superconformal point (rather that at the Coulomb branch) and how it interacts with the boundaries of the x^10. We find that the massless twisted states are not localized in the x^10. Instead, they are non-local meson-like composite particles comprised of a quark living at one boundary of the x^10, and antiquark living at the other boundary, and the string of strongly-interacting 5D gluons connecting the quark to the antiquark.