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.
Highlights
A continuum action can be rewritten as an action of lattice fields
The path integral is over these new variables
Gauge theories expressed in terms of Lie Algebra valued connections and supersymmetric theories are well defined on this lattice
Summary
A continuum action can be rewritten as an action of lattice fields. The path integral is over these new variables. Gauge theories expressed in terms of Lie Algebra valued connections and supersymmetric theories are well defined on this lattice. Long as the lattice remains infinite the lattice representation of the continuum action is exact. A continuum D dimensional field theory is turned into a D + 1 lattice field theory. The IR and UV problems look more symmetrical in this lattice form. UV and IR cutoffs are defined by limiting resolution. The index range on the D + 1-axis is bounded from above and from below respectively. The remaining directions remain infinite and D-space is not compactified
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