Quantum phase transition in many-flavor supersymmetric QED$_{3}$

Understand

We study $\mathcal{N}=4$ supersymmetric QED in three dimensions, on a three-sphere, with 2N massive hypermultiplets and a Fayet-Iliopoulos parameter.

• We identify the exact partition function of the theory with a conical (Mehler) function.
• This implies a number of analytical formulas, including a recurrence relation and a second-order differential equation, associated with an integrable system.
• In the large N limit, the theory undergoes a second-order phase transition on a critical line in the parameter space.