Perturbative analysis of twisted volume reduced theories

Understand

We discuss the perturbative expansion of SU(N) Yang-Mills theories defined on a d-dimensional torus of linear size l with twisted boundary conditions, generalizing previous results in the literature.

• For a specific class of twist tensors depending on a single integer flux value k, we show that perturbative results to all orders depend on the combination lN^(2/d) and a flux-dependent angle theta.
• This implies a new kind of volume independence that holds at finite N and for fixed values of theta.
• Our results also provide interesting information about the possible occurrence of tachyonic instabilities at one-loop order.