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.
Matrix Perturbation Theory For M-theory On a PP-Wave
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abstract
In this paper, we study the matrix model proposed by Berenstein, Maldacena, and Nastase to describe M-theory on the maximally supersymmetric pp-wave. We show that the model may be derived directly as a discretized theory of supermembranes in the pp-wave background, or alternatively, from the dynamics of D0-branes in type IIA string theory. We consider expanding the model about each of its classical supersymmetric vacua and note that for large values of the mass parameter \mu, interaction terms are suppressed by powers of 1/mu, so that the model may be studied in perturbation theory. We compute the exact spectrum about each of the vacua in the large \mu limit and find the complete (infinite) set of BPS states, which includes states preserving 2, 4, 6, 8, or 16 supercharges. Through explicit perturbative calculations, we then determine the effective coupling that controls the perturbation expansion for large \mu and estimate the range of parameters and energies for which perturbation theory is valid.
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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.
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.
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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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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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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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.