IIA and IIB spinors from K(E10)

TL;DR

This paper demonstrates how unfaithful spinor representations of K(E10) decompose to produce fermionic fields of both IIA and IIB supergravity, linking the algebraic structure to supergravity theories.

Contribution

It shows that a single K(E10) spinor representation can generate fermionic fields of both IIA and IIB supergravity through specific subgroup decompositions.

Findings

K(E10) spinors produce IIA and IIB fermions under different decompositions

The fermionic sector of the E(10)/K(E10) sigma-model captures supergravity fermions

Unified algebraic framework for IIA and IIB fermions from K(E10)

Abstract

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.