Chaos from Equivariant Fields on Fuzzy
arXiv:1806.10524 · doi:10.1007/JHEP12(2018)015
Abstract
We examine the Yang-Mills matrix model in -dimensions with gauge symmetry and a mass deformation term. We determine the explicit equivariant parametrizations of the gauge field and the fluctuations about the classical four concentric fuzzy four sphere configuration and obtain the low energy reduced actions(LEAs) by tracing over the s for the first five lowest matrix levels. The LEA's so obtained have potentials bounded from below indicating that the equivariant fluctuations about the do not lead to any instabilities. These reduced systems exhibit chaotic dynamics, which we reveal by computing their Lyapunov exponents.Using our numerical results, we explore various aspects of chaotic dynamics emerging from the LEAs. In particular, we model how the largest Lyapunov exponents change as a function of the energy. We also show that, in the Euclidean signature, the LEAs support the usual kink type soliton solutions, i.e. instantons in -dimensions, which may be seen as the imprints of the topological fluxes penetrating the concentric s due to the equivariance conditions, and preventing them to shrink to zero radius.
arXiv comment44+1 pages, 57 figures, expanded section on chaotic dynamics with new results, published version
References in corpus (40)
- M Theory As A Matrix Model: A Conjecture
- A bound on chaos
- Strings in flat space and pp waves from Super Yang Mills
- Black holes and the butterfly effect
- Fast Scramblers
- Matrix Perturbation Theory For M-theory On a PP-Wave
- Monte Carlo studies of supersymmetric matrix quantum mechanics with sixteen supercharges at finite temperature
- Black hole thermodynamics from simulations of lattice Yang-Mills theory
- On Finite 4D Quantum Field Theory in Non-Commutative Geometry
- Higher derivative corrections to black hole thermodynamics from supersymmetric matrix quantum mechanics
- On spherical harmonics for fuzzy spheres in diverse dimensions
- Noncommutative Gauge Theory on Fuzzy Four-Sphere and Matrix Model
- Longitudinal 5-branes as 4-spheres in Matrix theory
- Precision lattice test of the gauge/gravity duality at large-
- Evidence for fast thermalization in the plane-wave matrix model
- The BFSS model on the lattice
- Dynamical generation of fuzzy extra dimensions, dimensional reduction and symmetry breaking
- Chaos in Classical D0-Brane Mechanics
- To gauge or not to gauge?
- Chaos in the BMN matrix model
- Large N classical dynamics of holographic matrix models
- On the fermion spectrum of spontaneously generated fuzzy extra dimensions with fluxes
- Gauged And Ungauged: A Nonperturbative Test
- A Computer Test of Holographic Flavour Dynamics
- Lectures on Matrix Field Theory I
- Equivariant reduction of Yang-Mills theory over the fuzzy sphere and the emergent vortices
- Absence of a fuzzy phase in the dimensionally reduced 5d Yang-Mills-Chern-Simons model
- Construction of fuzzy S^4
- Toward Holographic Reconstruction of Bulk Geometry from Lattice Simulations
- The smallest matrix black hole model in the classical limit
- Black Hole Formation in Fuzzy Sphere Collapse
- Review of M(atrix)-Theory, Type IIB Matrix Model and Matrix String Theory
- One-loop stabilization of the fuzzy four-sphere via softly broken SUSY
- Equilibration in low-dimensional quantum matrix models
- Noncommutative Vortices and Flux-Tubes from Yang-Mills Theories with Spontaneously Generated Fuzzy Extra Dimensions
- Equivariant Reduction of U(4) Gauge Theory over S_F^2 x S_F^2 and the Emergent Vortices
- Emergent fuzzy geometry and fuzzy physics in dimensions
- New Fuzzy Extra Dimensions from Gauge Theories
- Equivariant Fields in an Gauge Theory with new Spontaneously Generated Fuzzy Extra Dimensions
- A Gauge Theory on Fuzzy Extra Dimensions