$E_8$ Gauge Theory and Gerbes in String T

Abstract

The reduction of the E 8 gauge theory to ten dimensions leads to a loop group, which in relation to twisted K-theory has a Dixmier-Douady class identified with the Neveu-Schwarz H-field. We give an interpretation of the degree two part of the eta form by comparing the adiabatic limit of the eta invariant with the one loop term in type IIA. More generally, starting with a G-bundle, the comparison for manifolds with String structure identifies G with E 8 and the representation as the adjoint, due to an interesting appearance of the dual Coxeter number. This makes possible a description in terms of a generalized Wess-Zumino-Witten model at the critical level. We also discuss the relation to the index gerbe, the possibility of obtaining such bundles from loop space, and the symmetry breaking to finite-dimensional bundles. We discuss the implications of this and we give several proposals.e-print archive: http://lanl.arXiv.org/abs/hep-th/0608190 400 HISHAM SATI

THE LOOP GROUP OF E8 AND TARGETS FOR SPACETIME

“…Mod 8 periodicity of structure: The observations in this note and in [1] imply similarities between worldvolume theories in the usual WZW constructions and spacetime theories. This suggests the mod 8 periodicity as indicated in the The second and third rows correspond, respectively, to going though the circle bundle first then taking the coboundary or to taking the coboundary first and then the circle bundle, arriving through both paths to the disk bundle, represented by the fourth row.…”

“…The analysis in [5] and the interpretation there and in [1] gives the scaling upward of the metric on the base to large volume as corresponding to the adiabatic limit. Alternatively one could look at the small volume limit of the fiber, i.e.…”

“…Over the base, the fields are then F ∈ Ω 2 (X 10 ; adP ) and φ ∈ Ω 0 (X 10 ; adP ). In our case the flatness condition F (A) = 0 does not come from self-duality as in [20] but rather from the requirement of Fourier decomposition [1]. The condition is the homotopy-flatness of the connection [19].…”

“…In the previous work [1] we studied the E 8 gauge theory over the circle part of the elevenmanifold, i.e. over the M-theory circle, making use of the Mickelsson construction [2] of (usual) WZW model on E 8 .…”

“…We also consider flat connections on the circle and their moduli space, which is just the circle itself via the holonomy. Next in section 5 we revisit the Higgs field considered in [1] in the sigma model context.…”