Off-Shell Supersymmetry Algebra in the Lorentzian IIB Matrix Model: Algebraic Constraints and a $κ$-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 $κ$-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.