Beta-function duality symmetry conjecture in the spin-boson model

Prove or refute that the weak–strong-coupling duality observed between intermediate-coupling fixed points in the SU(2)- and U(1)-symmetric spin-boson models is an exact symmetry of the renormalization-group beta function, and, if exact, derive the consequent mapping that predicts strong-coupling critical exponents from perturbative weak-coupling results.

Background

The paper presents numerical evidence for an approximate duality between weak- and strong-coupling fixed points (CR1/CR2 and QC1/QC2) in spin-boson models, noting that the product of the corresponding fixed-point couplings is nearly constant across a wide range of bath exponents. This suggests a deep structural relation in the renormalization-group flow.

Building on this observation and prior work, the authors note a conjecture that the duality is a symmetry of the beta function. They also point out that this duality becomes exact in the large-spin (S→∞) limit, but remains only approximate for S=1/2, leaving its exact status for finite S unresolved. Establishing or refuting this symmetry would clarify whether strong-coupling critical exponents can be predicted from weak-coupling perturbative results via duality.