  We introduce an effective theory with manifest particle-vortex symmetry for
disordered thin films undergoing a magnetic field-tuned
superconductor-insulator transition. The theory may enable one to access both
the critical properties of the strong-disorder limit, which has recently been
confirmed by Breznay et al. [PNAS 113, 280 (2016)] to exhibit particle-vortex
symmetric electrical response, and the nearby metallic phase discovered earlier
by Mason and Kapitulnik [Phys. Rev. Lett. 82, 5341 (1999)] in less disordered
samples. Within the effective theory, the Cooper-pair and field-induced vortex
degrees of freedom are simultaneously incorporated into an electrically-neutral
Dirac fermion minimally coupled to an (emergent) Chern-Simons gauge field. A
derivation of the theory follows upon mapping the superconductor-insulator
transition to the integer quantum Hall plateau transition and the subsequent
use of Son's particle-hole symmetric composite Fermi liquid. Remarkably,
particle-vortex symmetric response does not require the introduction of
disorder; rather, it results when the Dirac fermions exhibit vanishing Hall
effect. The theory predicts approximately equal (diagonal) thermopower and
Nernst signal with a deviation parameterized by the measured electrical Hall
response at the symmetric point.
