Unifying R-symmetry in M-theory

In this contribution we address the following question: Is there a group with a fermionic presentation which unifies all the physical gravitini and dilatini of the maximal supergravity theories in D=10 and D=11 (without introducing new degrees of freedom)? The affirmative answer relies on a new mathematical object derived from the theory of Kac--Moody algebras, notably E10. It can also be shown that in this way not only the spectrum but also dynamical aspects of all supergravity theories can be treated uniformly.Comment: 17 pages. Proceedings of ICMP 200

Biofueling rural development: making the case for linking biofuel production to rural revitalization

Biofuels play a crucial role in America\u27s quest for oil independence. In recent years, the biofuel industry has seen significant technology and efficiency advances, as well as expansions in the materials that can be used to create biofuels. Grains and oilseeds are limited in their ability to meet fuel needs, but a shift to biomass feedstocks offers better production possibilities. For rural communities, locally owned biomass refineries may offer promise of new investment, job growth, and revitalization

IIA and IIB spinors from K(E10)

We analyze the decomposition of recently constructed unfaithful spinor representations of K(E10) under its SO(9) x SO(9), and SO(9) x SO(2) subgroups, respectively, where K(E10) is the `maximal compact' subgroup of the hyperbolic Kac--Moody group E(10). We show that under these decompositions, respectively, one and the same K(E10) spinor gives rise to both the fermionic fields of IIA supergravity, and to the (chiral) fermionic fields of IIB supergravity. This result is thus the fermionic analogue of the decomposition of E(10) under its SO(9,9) and SL(9) x SL(2) subgroups, respectively, which yield the correct bosonic multiplets of (massive) IIA and IIB supergravity. The essentially unique Lagrangian for the supersymmetric E(10)/K(E10) sigma-model therefore can also capture the dynamics of IIA and IIB including bosons and fermions in the known truncations.Comment: 16 pages, v2: added paragraph on spinors for K(E9) and K(E11

Recognising a partitionable simplicial complex is in NP

We show that the problem of recognising a partitionable simplicial complex is a member of the complexity class NP, thus answering a question raised in [1

IIB supergravity and E10

We analyse the geodesic E10/K(E10) sigma-model in a level decomposition w.r.t. the A8xA1 subalgebra of E10, adapted to the bosonic sector of type IIB supergravity, whose SL(2,R) symmetry is identified with the A1 factor. The bosonic supergravity equations of motion, when restricted to zeroth and first order spatial gradients, are shown to match with the sigma-model equations of motion up to level four. Remarkably, the self-duality of the five-form field strength is implied by E10 and the matching.Comment: 14 page

Oxidizing Borcherds symmetries

The tensor hierarchy of maximal supergravity in D dimensions is known to be closely related to a Borcherds (super)algebra that is constructed from the global symmetry group E(11-D). We here explain how the Borcherds algebras in different dimensions are embedded into each other and can be constructed from a unifying Borcherds algebra. The construction also has a natural physical explanation in terms of oxidation. We then go on to show that the Hodge duality that is present in the tensor hierarchy has an algebraic counterpart. For D>8 the Borcherds algebras we find differ from the ones existing in the literature although they generate the same tensor hierarchy.Comment: 21 pages, 3 figures, 5 table

Loops in exceptional field theory

We study certain four-graviton amplitudes in exceptional field theory in dimensions $D\geq 4$ up to two loops. As the formulation is manifestly invariant under the U-duality group $E_{11-D}(\mathbb{Z})$, our resulting expressions can be expressed in terms of automorphic forms. In the low energy expansion, we find terms in the M-theory effective action of type $R^4$, $\nabla^4R^4$ and $\nabla^6 R^4$ with automorphic coefficient functions in agreement with independent derivations from string theory. This provides in particular an explicit integral formula for the exact string theory $\nabla^6 R^4$ threshold function. We exhibit moreover that the usual supergravity logarithmic divergences cancel out in the full exceptional field theory amplitude, within an appropriately defined dimensional regularisation scheme. We also comment on terms of higher derivative order and the role of the section constraint for possible counterterms.Comment: 1+78 pages: v2: Added references and typos corrected. Version accepted by JHEP. v3: corrected discussion of associativity in EFT and other typo

E10 Cosmology

We construct simple exact solutions to the E10/K(E10) coset model by exploiting its integrability. Using the known correspondences with the bosonic sectors of maximal supergravity theories, these exact solutions translate into exact cosmological solutions. In this way, we are able to recover some recently discovered solutions of M-theory exhibiting phases of accelerated expansion, or, equivalently, S-brane solutions, and thereby accommodate such solutions within the E10/K(E10) model. We also discuss the difficulties regarding solutions with non-vanishing (constant) curvature of the internal manifold.Comment: 16 pages, 1 figure. v2: Additional reference