Past exam of the mathematics course of the University of Cambridge 2015 iii Paper 48 2 d Solution Created 2026-10-03 Updated 2026-10-06
For ungauged chiral superfields, the two-derivative supersymmetric action is a real full-superspace integral plus a holomorphic half-superspace integral:The real Kähler potential determines the Kähler metric and kinetic terms; the superpotential determines Yukawa interactions and the F-term scalar potential. For canonical normalization, . Berezin integration is normalized to extract the highest component, , and the conjugate measure is chosen so the canonical term is . The D-term and F-term highest components vary by spacetime total derivatives, making the action invariant under supersymmetry. Gauging would replace the canonical bilinear by its gauge-covariant version and add a gauge kinetic F-term; no gauge multiplet is needed for the chiral theory here.