Supergravity couplings: a geometric formulation

TL;DR

This work develops a geometric, superspace-based framework for $D=4$, $N=1$ supergravity couplings to matter and Yang–Mills fields using $Kähler$ superspace geometry. It unifies gravity, matter, and gauge sectors through superfield rescalings and a Kahler potential, enabling ab initio $Kähler$ invariance and a canonical, rescaling-free Einstein term. The authors provide explicit superfield actions and their component-field realizations, derive equations of motion, and extend the formalism to include linear multiplets and Chern–Simons couplings, with applications to string-inspired effective theories. The formalism yields a coherent description of both F- and D-term structures, dualities between 2-form and chiral multiplets, and a natural treatment of non-holomorphic gauge couplings in a curved superspace setting. Overall, the geometric Kahler-superspace approach offers a compact, gauge-covariant route to constructing and analyzing $D=4$, $N=1$ supergravity theories with rich matter and tensor sectors, with clear implications for string theory compactifications and effective actions.

Abstract

This report provides a pedagogical introduction to the description of the general Poincare supergravity/matter/Yang-Mills couplings using methods of Kahler superspace geometry. At a more advanced level this approach is generalized to include tensor field and Chern-Simons couplings in supersymmetry and supergravity, relevant in the context of weakly and strongly coupled string theories.