Off-Shell Supersymmetry Algebra in the Lorentzian IIB Matrix Model: Algebraic Constraints and a $\kappa$-Minkowski-Like Sector

Abstract

The Lorentzian IIB matrix model provides a non-perturbative framework for emergent spacetime from matrix degrees of freedom. We study whether algebraic consistency constrains such structures by imposing restricted off-shell supersymmetry closure, modulo gauge transformations and explicitly identified trivial symmetries, on a CPT-even low-order effective-action ansatz with anisotropic background fields, without imposing their equations of motion. The zeroth-order Ward identity forces the scalar ansatz to be constant. At order two, retaining distinct macroscopic and internal transformation normalizations leads to a closure-compatible block-diagonal branch. On the nontrivial internal branch, Clifford-algebra identities force the internal non-Abelian flux to vanish. In four dimensions, a distinct dual-flux remainder can be absorbed into a Lorentz-type rotation when the macroscopic matrices form a non-degenerate coordinate sector. Within a linear absorption ansatz, the rank-three coefficient tensor is the Hodge dual of a vector. Macroscopic spatial isotropy selects its timelike orientation, yielding a $\kappa$-Minkowski-like algebra. Finite-dimensional Hermitian representations make the spatial sector trivial, so a nontrivial realization requires an infinite-dimensional limit with unbounded coordinate operators. The different weights of the spatial and internal generators under the adjoint action of $B_0$ are purely algebraic and are not interpreted as physical time evolution or dynamical compactification.

The views expressed are the author's own and do not necessarily reflect the official policy of the affiliated organization. This work is independent of official duties. v2: 18 pages. Final published version in Nuclear Physics B