The Large N Reduction in Matrix Quantum Mechanics -- a Bridge between BFSS and IKKT --

Abstract

The large N reduction is an equivalence between large N gauge theories and matrix models discovered by Eguchi and Kawai in the early 80s. In particular the continuum version of the quenched Eguchi-Kawai model may be useful in studying supersymmetric and/or chiral gauge theories nonperturbatively. We apply this idea to matrix quantum mechanics, which is relevant, for instance, to nonperturbative studies of the BFSS Matrix Theory, a conjectured nonperturbative definition of M-theory. In the bosonic case we present Monte Carlo results confirming the equivalence directly, and discuss a possible explanation based on the Schwinger-Dyson equations. In the supersymmetric case we argue that the equivalence holds as well although some care should be taken if the rotational symmetry is spontaneously broken. This equivalence provides an explicit relation between the BFSS model and the IKKT model, which may be used to translate results in one model to the other.

arXiv commentREVTeX, 4 pages with 3 figures

References in corpus (47)

• M Theory As A Matrix Model: A Conjecture
• String Theory Dynamics In Various Dimensions
• Bound States Of Strings And $p$-Branes
• A Large-N Reduced Model as Superstring
• Matrix String Theory
• D-brane field theory on compact spaces
• Noncommutative Yang-Mills in IIB Matrix Model
• Space-Time Structures from IIB Matrix Model
• Lattice Gauge Fields and Discrete Noncommutative Yang-Mills Theory
• Finite N Matrix Models of Noncommutative Gauge Theory
• Supersymmetry on a Spatial Lattice
• Supersymmetry on a Euclidean Spacetime Lattice I: A Target Theory with Four Supercharges
• Nonperturbative Dynamics of Noncommutative Gauge Theory
• A Lattice Formulation of Super Yang-Mills Theories with Exact Supersymmetry
• Dynamical Aspects of Large N Reduced Models
• Supersymmetry on a Euclidean Spacetime Lattice II: Theories with Eight Supercharges
• Black hole-black string phase transitions in thermal 1+1-dimensional supersymmetric Yang-Mills theory on a circle
• Dynamical Generation of Four-Dimensional Space-Time in the IIB Matrix Model
• Super Yang-Mills Theories on the Two-Dimensional Lattice with Exact Supersymmetry
• Monte Carlo Studies of the IIB Matrix Model at Large N
• A new approach to the complex-action problem and its application to a nonperturbative study of superstring theory
• Large N reduction in the continuum three dimensional Yang-Mills theory
• Large N Dynamics of Dimensionally Reduced 4D SU(N) Super Yang-Mills Theory
• Mean Field Approximation of IIB Matrix Model and Emergence of Four Dimensional Space-Time
• Does the crossover from perturbative to nonperturbative physics in QCD become a phase transition at infinite N ?
• Spontaneous Breakdown of Lorentz Invariance in IIB Matrix Model
• A geometrical approach to N=2 super Yang-Mills theory on the two dimensional lattice
• Lattice Supersymmetry and Topological Field Theory
• Various Super Yang-Mills Theories with Exact Supersymmetry on the Lattice
• Brane world from IIB matrices
• Finite Yang-Mills Integrals
• Improved Perturbation Theory and Four-Dimensional Space-Time in IIB Matrix Model
• Lattice formulation of $\mathcal{N}=4$ super Yang-Mills theory
• Effective Actions of Matrix Models on Homogeneous Spaces
• Chiral symmetry breaking at large N_c
• Proposal for the numerical solution of planar QCD
• Exactly Solvable Matrix Models for the Dynamical Generation of Space-Time in Superstring Theory
• Geometry of Reduced Supersymmetric 4D Yang-Mills Integrals
• On the Spontaneous Breakdown of Lorentz Symmetry in Matrix Models of Superstrings
• Dijkgraaf-Vafa theory as large-N reduction
• The quark mass dependence of the pion mass at infinite N
• Stability of fuzzy $S^2\times S^2$ geometry in IIB matrix model
• Stability of Fuzzy S^2 x S^2 x S^2 in IIB Type Matrix Models
• Rotational Symmetry Breaking in Multi-Matrix Models
• Large Nc Continuum Reduction and the Thermodynamics of QCD
• Towards the lattice study of M-theory (II)
• Semiclassical Geometry of 4D Reduced Supersymmetric Yang-Mills Integrals

Cited by in corpus (7)

• Non-lattice simulation for supersymmetric gauge theories in one dimension
• A non-perturbative study of 4d U(1) non-commutative gauge theory -- the fate of one-loop instability
• Phase structure of matrix quantum mechanics at finite temperature
• Dynamical aspects of the plane-wave matrix model at finite temperature
• Exact fuzzy sphere thermodynamics in matrix quantum mechanics
• Perturbative Vacua from IIB Matrix Model
• Replicas, averaging and factorization in the IIB matrix model