The Flux Problem is a famous problem in condensed matter physics, solved by Lieb. It states that the magnetic flux through each plaquette of a square lattice in 2d (with either OBC/PBC or PBC/PBC) that minimizes the ground state energy of a system of free electrons at half-filling is . Such phase, called -Flux Phase, is known to display emergent Dirac-like low energy excitations. What happens when we couple the system to a dynamical 2 gauge field whose energy is minimized by 0 flux per plaquette? In this talk, we prove the stability of -Flux Phase by showing, using Reflection Positivity techniques, that the energy of the fermions at half-filling in a background of N monopoles increases extensively in N. As an application, we compute explicitly the zero temperature diamagnetic susceptibility and the conductivity of the gauge theory, and we show that they coincide with the ones of massless Dirac fermions. Arxiv: https://arxiv.org/abs/2501.10065 (Join Work with Marcello Porta)