Conformal Field Theory in Magnetic Field

External probes of conformal field theories (CFTs) give rise to novel observables and enable new ways to understand CFTs. Famous examples include CFTs in curved space, non-zero temperature, and non-zero chemical potential. Essential in this understanding is the role of low-energy effective actions, which can be constructed based on symmetry principles. In this talk, we will discuss three-dimensional CFTs with global symmetry in a background magnetic field. Assuming a gapped phase in the presence of the magnetic field, we will discuss the corresponding effective action and two-point functions of the conserved current and stress-energy tensor that can be defined using it. Using dispersive arguments, we will derive constraints on the effective action coefficients and discuss their consequences for physical quantities of interest.