Past exam of the mathematics course of the University of Cambridge 2001 iii Paper 65 1 v Solution Created 2026-10-03 Updated 2026-10-14
Specify the gauge group, its gauge group representations and gaugings, a real Kähler potential , a holomorphic superpotential , and a symmetric holomorphic gauge kinetic function , with positive kinetic matrices. The latter includes the gauge couplings and theta angles; allowed Abelian Fayet–Iliopoulos terms require constants . For local supersymmetry, also specify the Planck mass; constant Fayet–Iliopoulos terms in conventional N=1 supergravity require a compatible gauged R-symmetry and transformation of . and are holomorphic; generally is not. Radiative corrections generally change . The Wilsonian effective action obeys superpotential non-renormalization perturbatively, although physical couplings run through field normalization and nonperturbative corrections can change . The gauge kinetic function does receive corrections while remaining holomorphic; its perturbative Wilsonian running has one-loop exactness of the holomorphic gauge kinetic function, not all-order constancy of the physical gauge coupling.