On six dimensional "gauge" theories with irrational theta angle

A recent proposal for 6d "gauge" theories with rational theta angle is discussed. These theories were constructed from n_C coinciding (p, q) 5-branes of IIB in the limit of vanishing string constant. They have (1,1) supersymmetry and the low energy theory is 6d Yang-Mills with gauge group SU(n_c) and a rational theta angle θ₆/2π = f/q, where fp = 1 (mod q). By changing the point of view, considering the (p, q) 5-branes to be D5-branes, the 6d theta angle is identified with a 10d theta angle. This point of view together with some assumptions suggests a generalization of the previous limit to arbitrary theta. This limit seems to define a decoupled 6d theory even though the 10d theory does not become free in general.