Loop Groups and Spacetime Sigma Models

We propose a sigma model with target space E8 where the ten-dimensional spacetime plays the role of the worldsheet. This is motivated first by the E8 gauge theory in eleven dimensions which leads to a loop group description in ten dimensions, and second by a reduction a la’ Bershadsky-Johansen-Sadov-Vafa. We explore some consequences of this proposal such as possible Lagrangians and existence of flat connections. We make observations on the homotopy and cohomology structure (at primes 2 and 3) of E8 which reveal interesting possibilities, one of which relates to theories in eighteen and twenty-six dimensions. E-mail: [email protected]