Shyamoli Chaudhuri

Matrix Theory and the Fundamental Symmetry $D_{11}\times \mathcal{E}_{8}\times \mathcal{E}_{8}$: A Planck Scale Generalized Electric-Magnetic Dual Initial State



Abstract

We sketch the line of reasoning that leads out from Peter West's well-established result in 2001-04, motivated by the exciting developments in generalized electric magnetic duality in the worldsheet formalism, identifying theories with 32 supercharges by the global symmetry group, $E_{11}$, demonstrating an explicit isomorphism to $E_{11}$ of each of the four theories with 32 supercharges: 11d supergravity, and the type IIA and type IIB, and massive type IIA theories. In subsequent work I have shown that this leads to the group $D_{11}$ for the chiral type IA, type IB, and heterotic anomalous supergravities, and anomaly cancelation with the introduction of Yang-Mills fields completes our identification of the fundamental symmetry group of String/M theory with sixteen conserved supercharges as: $D_{11}\times \mathcal{G}_{\text{Yang-Mills}}$, where $\mathcal{G}_{\text{Yang-Mills}}$ is the affine extension of $E_{8}\times E_{8}$ or $Spin(32)/\mathbb{Z}_{2}$; not the group $B_{11}$, suggested by Schnakenburg and West. Comparison of the half BPS states of this algebra, including both massive modes in the Kac Moody Algebra and the higher levels of the very extended group, with the BPS algebras of N=8 and N=4 string theories, using the partially complete 1993-96 pioneering analyses by Gregory Moore, and by Jeffrey Harvey and Moore, followed by many authors, of N=2 heterotic strings, which bring in many subtle new features, would give complementary insight, and enable significant progress leading from West's intriguing results for thesymmetry group of M theory. We sketch the implications for a straightforward matrix realization of a theory with this algebra demonstrating emergent spacetime, the early beginnings of an expanding universe cosmology, and chiral matter, incorporating also the principle of generalized 11d Hodge-Poincare electric-magnetic duality. We identify the Planck scale patch of initial state spacetime-matter with a massive monopole carrying all six species of generalized electric-magnetic charge, in a fundamental theory which incorporates generalized electric-magnetic duality in its initial conditions.