Five-dimensional gauge theories on spheres with negative couplings

Authors: Joseph A. Minahan and Anton Nedelin Preprint number: UITP-23/20 We consider supersymmetric gauge theories on S^5 with a negative Yang-Mills coupling in their large N limits. Using localization we compute the partition functions and show that the pure SU(N) gauge theory descends to an SU(N/2)_{N/2}×SU(N/2)_{−N/2}× SU(2) Chern-Simons gauge theory as the inverse ’t Hooft coupling is taken to negative infinity for N even. The Yang-Mills coupling on the SU(N/2)_{±N/2} is infinite, while that on the SU(2) goes to zero. We also show that the odd N case has somewhat different behavior. We then study the SU(N/2)_{N/2} pure Chern-Simons theory. While the eigenvalue density is only found numerically, we show that its width equals 1 in units of the inverse sphere radius, which allows us to find the leading correction to the free energy when turning on the Yang-Mills term. We then consider USp(2N) theories with an antisymmetric hypermultiplet and N_f < 8 fundamental hypermultiplets and carry out a similar analysis. We present evidence that the USp(2N) theories have a fifth order phase transition in the inverse coupling at their superconformal fixed point. Along the way we show that the one-instanton contribution to the partition function remains exponentially suppressed at negative coupling for the SU(N) theories in the large N limit.