The Pfaffian phase in BFSS becomes an O(9) pseudoscalar operator in a bosonic matrix integral, requiring 10-loop order in the high-T expansion before the sign problem is detectable in the 't Hooft regime.
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M Theory As A Matrix Model: A Conjecture
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abstract
We suggest and motivate a precise equivalence between uncompactified eleven dimensional M-theory and the N = infinity limit of the supersymmetric matrix quantum mechanics describing D0-branes. The evidence for the conjecture consists of several correspondences between the two theories. As a consequence of supersymmetry the simple matrix model is rich enough to describe the properties of the entire Fock space of massless well separated particles of the supergravity theory. In one particular kinematic situation the leading large distance interaction of these particles is exactly described by supergravity . The model appears to be a nonperturbative realization of the holographic principle. The membrane states required by M-theory are contained as excitations of the matrix model. The membrane world volume is a noncommutative geometry embedded in a noncommutative spacetime.
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A double-scaling large-d saddle for mass-deformed BFSS/BMN matrix QM interpolates between commutator-dominated and mass-dominated regimes, yielding BFSS_{2}-like low-T uniform-holonomy dynamics and IKKT-like high-T almost-commuting behavior.
The bosonic AdS3/CFT2 duality emerges from the Gross-Neveu model via higher-spin composites and fluctuations in competing spin-0 and spin-1 condensates that define the radial bulk coordinate.
The free particle, harmonic oscillator, and inverted oscillator are unified as parabolic, elliptic, and hyperbolic realizations of the same conformal module, with explicit mappings between their states, coherent states, and scattering data via metaplectic rotations and Mellin transforms.
New positivity constraints from open bubbles and color matrices provide sharp bounds on unitary tensor integrals at finite N and probe deviations from Gaussian universality.
SO(d) and O(d) invariant sectors of d-matrix QM show negative microcanonical heat capacity that becomes positive at k_crit ~ N^2/4, forming a caloric fold similar to AdS black holes.
Q-cohomology in BMN matrix QM is mass-flow invariant via a similarity transformation of the nilpotent supercharge component.
Non-renormalization in UV 2D SYM fixes the Wilson coefficient of the DVV operator in the IR orbifold CFT, consistent with matrix string theory.
In reduced BMN matrix models, Lanczos coefficients scale linearly with the mass parameter, producing quadratic corrections to early-time Krylov complexity growth at the same order for both state and operator versions.
Finite-N BMN index summed over all vacuum sectors for N≤9 reveals order-N² entropy growth that survives the sum and dominance switching from single- to double-partition sectors starting at N=5.
Microscopic D-brane description of non-supersymmetric extremal black holes yields a unique ground state with non-zero energy, confirming absence of degeneracy.
Develops worldsheet sigma model for fundamental strings in critical type IIA limit showing nodal singularities and derives T-duality web unifying decoupling limits including ambitwistor and Carrollian strings.
Inner horizon saddles supply the semiclassical correction -exp(A_inner/4G) to near-extremal black-hole entropy and motivate a spectral KSW criterion for well-defined one-loop effects around complex gravitational saddles.
The very-low-temperature bosonic singlet spectrum in BFSS_{d+1} is controlled by d(d+1)/2 quadratic Gram operators Tr(X_a X_b), with an exact BFSS_3 = (BFSS_2)^3 factorization at (d,N)=(2,2).
Carrollian fermion actions are obtained from relativistic Dirac theory via c-expansion and connected to light-cone dynamics through co-dimension one Carroll subalgebras in the Poincaré algebra.
A regularization technique based on Berezin-Toeplitz quantization is introduced to represent curved spacetimes such as tori and the two-sphere with finite matrices in the type IIB matrix model.
In the semiclassical approximation the eigenvalues of the SU(N) matrix model Hamiltonian converge one-to-one to the eigenvalues of the continuum supermembrane Hamiltonian with central charge as N approaches infinity.
Conjugation deformations preserve normalizability in the BMN matrix model, implying BPS states do not lift and their unsigned number is invariant except at the free and BFSS points.
Off-shell supersymmetry closure in the Lorentzian IIB matrix model algebraically decouples the internal sector and selects a κ-Minkowski-like algebra in the macroscopic four-dimensional sector when spatial isotropy is imposed.
Establishes equivalence between endpoint and Molien-Weyl formulations for large-d BFSS models on the lattice and derives finite continuum D-channel via a toy holonomy potential model.
A simplified mini-BMN matrix model for a radiating black hole exhibits early-time chaotic growth of Krylov complexity followed by late-time saturation to a plateau consistent with equilibration.
A regularized finite-dimensional master field numerically solves large-N reduced matrix models, reproducing exact Euclidean solutions and perturbative Minkowski results for one- and two-matrix cases.
A tachyonic AdS/QCD construction deforms the bulk geometry with a tachyon-dependent dielectric function to produce a unified running coupling from perturbative UV to nonperturbative IR regimes.
In this fuzzy-sphere matrix model the largest Lyapunov exponent drops to zero at finite temperature, respecting the Maldacena-Shenker-Stanford bound while entanglement shows fast scrambling.
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Noncommutative Gauge Theories and Gravity
The paper reviews gauge-theoretic formulations of gravity in ordinary and noncommutative spaces based on the authors' earlier works.