arXiv subjects

Tetsuyuki Muramatsu

Publications and source records attributed to Tetsuyuki Muramatsu.

4 recordsLinked to original sources

arXiv2026

Pfaffian sensitivity to temporal deformations of an N=5 background in the Lorentzian IIB matrix model

How spacetime dimensionality and anisotropy emerge from matrix degrees of freedom is a central question in the IIB matrix model. Our previous work constructed a family of constrained classical solutions at $N=5$, including a reference configuration with vanishing temporal extent and a pre-existing $3+6$ spatial hierarchy. Here we examine how the fermionic Pfaffian responds to temporal-matrix deformations of this configuration. The background geometry determines a distinguished real two-plane of temporal deformations. Numerical analysis of the full fermionic operator shows that the sensitivity of its lowest positive-eigenvalue doublet is strongly concentrated in this plane and dominates the first-order Pfaffian response. Under stated reflection-covariance and nonsingularity conditions, the other local one-loop contributions cancel at first order when combined, so the gradients of the logarithmic magnitudes of the total local one-loop weight and the Pfaffian agree. We prescribe a temporal deformation along the projection of this gradient onto the two-plane and determine the remaining matrix components by conditional classical stationarity. The existing spatial hierarchy is modestly strengthened at quadratic order, while the spectrum changes little at the small amplitude considered. This quadratic response is independent of orientation within the plane, although the first-order Pfaffian response distinguishes such orientations. These results connect background geometry, fermionic spectral sensitivity, and conditional classical spatial anisotropy.

hep-th↗

arXiv2026

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

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.

hep-th↗

arXiv2026

One-Loop Fluctuation Response Along a Constrained Noncommutative Modulus in the Lorentzian IIB Matrix Model

We study a local constrained problem at matrix size $N=5$ in the Lorentzian IIB (IKKT) matrix model and numerically continue a one-dimensional physical modulus. For an exact fixed-$Q_ρ$ constrained solution family, the stationary identity implies constant classical action; the 23 accepted backgrounds realize this relation to the quoted precision. Across the sampled branch, the spectrum of the Lorentzian extent operator remains common to numerical precision while microscopic noncommutative invariants vary. We evaluate finite-dimensional one-loop fluctuations along this branch. At fixed bosonic background, the fermionic Grassmann integral is exact and gives $\operatorname{Pf}\mathcal M_F$; its magnitude is invariant under color-gauge and connected proper-Lorentz transformations and varies along the modulus. The complete boson--ghost--fermion quotient measure defines a Lorentz-representative-independent density one-form rather than a scalar potential. Thus quantum fluctuation data distinguish backgrounds unresolved by the coarse quadratic spectrum. We also apply a framed higher-$L$ SO(5) structural probe. At the reference background, the ordered $3+6$ spectral separation is larger at $L=2,3$ than at $L=1$, and larger still in the canonical large-$L$ limit. This is a frame-defined diagnostic, not an intrinsic observable or a higher-$N$ solution. The Pfaffian and higher-$L$ responses are closely correlated along the sampled branch, which we treat only as descriptive. These results suggest that microscopic noncommutative structure and quantum fluctuations may contain information relevant to dimensional dynamics, without establishing dimensional selection.

hep-th↗

arXiv2026

Supersymmetric Origin of Four-Dimensional Space-time in the IIB Matrix Model

We investigate the constraints imposed by supersymmetry on the IIB matrix model (IKKT model) by requiring both the closure of the transformations and the satisfaction of the Ward identities at the leading order of the order expansion. Following the systematic methodology, we evaluate the most general forms of the effective action and supersymmetry transformations consistent with the $SU(N)$ algebra. In ten dimensions, we prove that these supersymmetric requirements lead to a non-renormalization theorem, which forces all coefficient functions to be constant. This result stems from the emergence of a 5-form tensor in the closure condition that cannot be absorbed by the $SU(N)$ algebra. This residual term strictly forbids non-trivial fluctuations at the leading order. While a similar non-renormalization theorem holds in four dimensions, we demonstrate that the four-dimensional Clifford algebra provides a unique exit through Hodge duality. This duality geometrically maps the anomalous high-rank tensor structures into absorbable lower-rank forms, allowing for non-trivial dynamical backgrounds prohibited in ten dimensions. We find that such non-trivial solutions are restricted to (anti-)self-dual configurations, which, through reality conditions, necessitate a Euclidean metric. Our results indicate that the emergence of a four-dimensional Euclidean space-time is a prerequisite for the theory to admit non-trivial backgrounds while preserving supersymmetry at the leading order.

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