Effective Gravitational Couplings of Kaluza-Klein Gauge Theories

Abstract: We study the effective gravitational couplings of four-dimensional Kaluza-Klein compactified gauge theories with eight supercharges. The class of theories we consider are the pure SU(N) Yang-Mills theories at admissible Chern-Simons levels and the conformal gauge theories with 2N fundamental flavours. The resolvent of the gauge theory plays a crucial role in the calculation of these gravitational couplings. The results obtained from the Seiberg-Witten geometry are matched against independent computations using localisation.