Modern Tensor-Spinor Symbolic Algebra Algorithms and Computing Non-Closure Geometry&Holoraumy in 11D, N = 1 Supergravity

A long-standing question in supergravity is whether 11D, N = 1 supergravity can be made off-shell, precisely along the lines of 4D, N = 1 superfield supergravity. Experience with supersymmetry theories like the 4D double-tensor multiplet indicates that such off-shell SUSY problems are intimately tied with the non-closure functions of the multiplet. Motivated by this link, we explore a formulation of the 11D supergravity multiplet especially useful for non-closure geometry computations, and we undertake a detailed derivation of the associated non-closure functions. In addition, we use this formulation to compute the on-shell holoraumy of the multiplet. We show that this holoraumy carries no so-called ``electromagnetic-duality rotations,"proving that 11D supergravity provides a counterexample to the ubiquity of such rotations in holoraumy previously conjectured based on 4D calculations. These results are all achieved using a suite of new symbolic algebra algorithms, implemented in Cadabra. This includes a purely symbolic implementation of the algebra/canonicalization of spinor-indexed tensor expressions, including automatic simplification following NW-SE convention and more versatile Fierz expansion tools. We also provide algorithms solving for unknown parameters in multiplets' supersymmetry transformation rules by leveraging superalgebra closure and action SUSY-invariance requirements, as well as an algorithm computing holoraumy, all without use of any explicit matrix representation.