Logarithmic moduli of roots of line bundles on curves

We use the theory of logarithmic line bundles to construct compactifications spaces roots a bundle on family curves, generalising work number authors. This runs via study torsion in tropical and jacobians (recently constructed by Molcho Wise). Our moduli space carries ‘double ramification cycle’ measuring locus where given root is isomorphic trivial bundle, we give tautological formula for this class language piecewise polynomial functions (as recently developed Molcho–Pandharipande–Schmitt Holmes–Schwarz).