Boson–fermion duality in a gravitational background

摘要: Abstract We study the 2+1 dimensional boson–fermion duality in presence of background curvature and electromagnetic fields. The main players are, on one hand, a massive complex | ϕ 4 scalar field coupled to U ( 1 ) Maxwell–Chern–Simons gauge at level 1, representing relativistic composite boson with unit attached flux, other Dirac fermion. show that, curved partition function, boson, infinite coupling limit, is dual short-range interacting gravitational spin connection arises naturally from factors Wilson loop Chern–Simons theory. A non-minimal included bosonic side order obtain agreement between functions. Although an explicit Lagrangian expression for fermionic interactions not obtained, their nature constrains them be irrelevant, which protects its strong interpretation as exact mapping IR fixed point Wilson–Fisher–Chern–Simons free also even away IR, keeping term key importance it provides necessary prevent intersections worldlines path integral, thus forbidding unknotting knots ensuring preservation worldline topologies.