Holographic Krylov complexity in the Coulomb branch of $\mathcal{N}=4$ SYM

Abstract

We study holographic Krylov complexity in the Coulomb branch of $\mathcal{N}=4$ SYM. Adopting the proposal that the time derivative of the Krylov complexity is dual to the proper radial momentum of a massive particle, we investigate two probe geodesics within this geometry. For one of the radial trajectories we obtain exact analytic results, even when additional motion in the internal space is included. In cases where the geodesic avoids the interior curvature singularity, the Krylov complexity exhibits oscillatory behavior, with a frequency governed by the Coulomb scale and an amplitude determined by the UV cutoff, the Coulomb scale, and the angular momentum. This oscillatory pattern is lost, when the radial trajectory is approaching the singularity. Finally, we compare our holographic results with field-theoretic calculations, finding qualitative agreement.

arXiv comment20 pages, 7 figures, matches published version in JHEP

References in corpus (11)

• Deforming field theories with $U(1)\times U(1)$ global symmetry and their gravity duals
• The Coulomb Branch of Gauge Theory from Rotating Branes
• Continuous distributions of D3-branes and gauged supergravity
• Quantum Dynamics in Krylov Space: Methods and Applications
• Supersymmetric solitons and a degeneracy of solutions in AdS/CFT
• New Compactifications of Supergravities and Large N QCD
• Quantum complexity in gravity, quantum field theory, and quantum information science
• Gravity duals for the Coulomb branch of marginally deformed N=4 Yang-Mills
• On supersymmetry and other properties of a class of marginally deformed backgrounds
• Complexity and Operator Growth in Holographic 6d SCFTs
• Krylov Complexity Meets Confinement