In BFSS matrix theory, the sign problem is nonzero at large N but first appears at 10-loop order, giving ⟨cosθ⟩ ≈ exp(−9×10⁻⁹ N²(λβ³)⁵).
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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 bootstrap SDP with a dual 'inequalities of motion' formulation rigorously bounds Euclidean two-point correlators and extracts the low-lying adjoint spectrum of one-matrix quantum mechanics.
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.
A finite-dimensional regularized master field that minimizes residual loop equations reproduces exact Euclidean and perturbative Minkowski results for one- and two-matrix models.
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.
In SO(d)- and O(d)-invariant sectors of the U(N) d-matrix harmonic oscillator, microcanonical heat capacity is negative at low energy and turns positive at kcrit ~ N^2/4, producing a caloric fold analogous 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.
The paper proposes that condensate competition in the 2d Gross-Neveu model generates an emergent AdS₃ bulk, a higher-spin tower, D1-branes, and linearized Einstein gravity with G₃ = ℓ_AdS/4πN².
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.
Gram/Wishart/Stiefel reformulation of N=2 large-d BFSS/BMN endpoints absorbs -A into a shifted mass and recovers the universal continuum -2d DΛ-channel after non-polynomial transverse completion.
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 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.
citing papers explorer
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An effective field theory approach to the sign problem in BFSS
In BFSS matrix theory, the sign problem is nonzero at large N but first appears at 10-loop order, giving ⟨cosθ⟩ ≈ exp(−9×10⁻⁹ N²(λβ³)⁵).
-
Bootstrapping Euclidean Two-point Correlators
A bootstrap SDP with a dual 'inequalities of motion' formulation rigorously bounds Euclidean two-point correlators and extracts the low-lying adjoint spectrum of one-matrix quantum mechanics.
-
The Free Particle--Oscillator--Inverted Oscillator Triangle: Conformal Bridges, Metaplectic Rotations and $\mathfrak{osp}(1|2)$ Structure
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.
-
Regularized Master-Field Approximation for Large-$N$ Reduced Matrix Models
A finite-dimensional regularized master field that minimizes residual loop equations reproduces exact Euclidean and perturbative Minkowski results for one- and two-matrix models.
-
Additional constraints for the tensor bootstrap
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.
-
Negative heat capacities in spherically symmetric sectors of $d$-matrix quantum mechanics
In SO(d)- and O(d)-invariant sectors of the U(N) d-matrix harmonic oscillator, microcanonical heat capacity is negative at low energy and turns positive at kcrit ~ N^2/4, producing a caloric fold analogous to AdS black holes.
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Mass-Flow Invariance of $Q$-Cohomology in BMN Matrix Quantum Mechanics
Q-cohomology in BMN matrix QM is mass-flow invariant via a similarity transformation of the nilpotent supercharge component.
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Wilson coefficients from a non-renormalization theorem in 2D SYM
Non-renormalization in UV 2D SYM fixes the Wilson coefficient of the DVV operator in the IR orbifold CFT, consistent with matrix string theory.
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Krylov Complexity for Plane Wave Matrix Model
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.
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Finite-$N$ BMN index across all vacuum sectors
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.
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Higher-spin composites and emergent AdS$_3$ geometry in the $(1+1)$-dimensional Gross-Neveu model
The paper proposes that condensate competition in the 2d Gross-Neveu model generates an emergent AdS₃ bulk, a higher-spin tower, D1-branes, and linearized Einstein gravity with G₃ = ℓ_AdS/4πN².
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An extremal black hole with a unique ground state
Microscopic D-brane description of non-supersymmetric extremal black holes yields a unique ground state with non-zero energy, confirming absence of degeneracy.
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Worldsheet Formalism for Decoupling Limits in String Theory
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.
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Inner Horizon Saddles and a Spectral KSW Criterion
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.
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Molien--Weyl Singlet Counting and BFSS$_2$--Factorization in Gaussian Matrix QM
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).
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Carroll fermions, expansions and the lightcone
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.
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Gram--Wishart--Stiefel formulation of the $N=2$, large--$d$ gauge theory in 1D
Gram/Wishart/Stiefel reformulation of N=2 large-d BFSS/BMN endpoints absorbs -A into a shifted mass and recovers the universal continuum -2d DΛ-channel after non-polynomial transverse completion.
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Description of curved spacetimes by finite-size matrices in the type IIB matrix model
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.
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On the large N convergence of matrix models
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.
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BPS Non-Renormalization in the BMN Matrix Model
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.
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Off-Shell Supersymmetry Algebra in the Lorentzian IIB Matrix Model: Algebraic Constraints and a $\kappa$-Minkowski-Like Sector
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.
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Endpoint formulation and Molien--Weyl structure for the \(N=2\), large--\(d\) BFSS/BMN models
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.
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Krylov complexity from a simple quantum mechanical model for a radiating black hole
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.
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Tachyonic AdS/QCD, Determining the Strong Running Coupling and \beta-function in both UV and IR Regions of AdS Space
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.
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Real-Time Quantum Dynamics on the Fuzzy Sphere: Chaos and Entanglement
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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Uni-vector deformations, D0-bound states and DLCQ
Uni-vector deformations in Type IIA map D0 backgrounds to themselves and generate F1-D0 and D2-D0 bound states while relating to DLCQ of M-theory.
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Exponentially Long Evaporation of Noncommutative Black Hole
Noncommutative spacetime shifts the collapsing shell proportionally to outgoing Hawking mode momentum, invalidating standard robustness arguments and causing radiation to decay exponentially after scrambling for exponentially long black hole evaporation.
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Multi-Matrix Quantum Mechanics, Collective Fields and Emergent Space
Derives the effective Hamiltonian in the collective field framework for three-matrix quantum mechanics models and analyzes the stability of the vacuum solution.
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Quantum spacetime and quantum fluctuations in the IKKT model at weak coupling
In the IKKT matrix model, quantum fluctuations are negligible compared to noncommutativity scales at weak coupling for Moyal-Weyl and covariant quantum spacetime backgrounds, justifying semi-classical emergent geometry.
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Fermionic modes of D-instanton wormholes from broken local supersymmetry
Broken local supersymmetry modes in D-instanton wormholes deliver fermionic boundary modes through current-current two-point functions on tree-level cylinder geometry.
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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.
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The Carrollian Kaleidoscope
A review summarizing Carrollian symmetries, CCFT constructions, and applications in AFS holography, Carroll hydrodynamics, and condensed matter phenomena such as fractons and flat bands.
- A Double--Scaling Large--\(d\) Saddle of BFSS/BMN Matrix Quantum Mechanics
- What does it mean to have a quantum gravitational theory of de Sitter Space?