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

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