TL;DR
This paper explores how expanding continuous fields in wavelet bases transforms continuum actions into higher-dimensional lattice actions, revealing new criteria for acceptable actions in lattice field theory.
Contribution
It introduces a novel approach linking wavelet expansions to lattice formulations of field theories, especially in the context of Euclidean AdS spaces.
Findings
Wavelet expansion maps D-dimensional continuum actions to (D+1)-dimensional lattice actions.
New criteria for acceptable lattice actions are proposed based on this mapping.
Potential applications in AdS/CFT and lattice field theory are suggested.
Abstract
When continuous fields are expanded in a wavelet basis, a D-dimensional continuum action becomes a (D+1)-dimensional lattice action on the naively discretized Poincare-patch coordinates of an Euclidean AdS(D+1). New possible criteria for acceptable actions open up.
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