2026/08/03 by Colleen Delaney, Calvin McPhail-Snyder
Mathematics · Physics and Astronomy · #math.QA #math-ph #math.GT #math.MP #msc:57K16 #msc:18M20 #msc:57K12
44 pages, many figures
arxiv created 2026/08/03 · arxiv updated 2026/08/05
We show that the computational complexity of Reshetikhin-Turaev invariants of simply colored links is preserved when their underlying ribbon fusion categories are related by the zesting construction. Zesting modifies an A-graded ribbon fusion category C with additional algebraic data ζ to produce a new category Cζ whose link invariants are known to differ from those of C by an invariant of A-colored links Jζ depending only on ζ. Building on this understanding and on earlier work on quantum braid group representations under zesting, our result suggests how zesting contributes to the organization of (2+1)D topological quantum field theories and topological phases into complexity-theoretic hierarchies. To prove our main result we develop a local formalism analogous to the Reshetikhin-Turaev construction to compute tangle invariants Jζ(T), which leads to a polynomial time algorithm to compute invariants of links Jζ(L). A byproduct of our construction is an identification (up to a sign) of the link invariants Jζ(L) as rack cocycle invariants, which may be of independent interest. Our formalism also extends to define invariants of closed 3-manifolds with A-structure and we obtain similar complexity results for homotopy quantum field theories built from A-modular fusion categories.