Hamiltonian Superfield Formalism with N Supercharges

TL;DR

This paper introduces a unified action principle for any number of supercharges in supersymmetric theories, revealing new features like the Pfaffian measure as a Gaussian integral and a superfield formulation with a covariant heta-space.

Contribution

It proposes a universal action principle for arbitrary N supercharges and reinterprets the supersymmetry algebra as a symplectic structure on fermionic space.

Findings

The Pfaffian measure arises from Gaussian integration over superpartners.

The formulation is independent of the choice of direction n^a in heta-space.

A covariant superfield formulation with a symplectic structure is developed.

Abstract

An action principle that applies uniformly to any number N of supercharges is proposed. We perform the reduction to the N=0 partition function by integrating out superpartner fields. As a new feature for theories of extended supersymmetry, the canonical Pfaffian measure factor is a result of a Gaussian integration over a superpartner. This is mediated through an explicit choice of direction n^a in the \theta-space, which the physical sector does not depend on. Also, we re-interpret the metric g^{ab} in the Susy algebra [D^a,D^b] = g^{ab}\partial_t as a symplectic structure on the fermionic \theta-space. This leads to a superfield formulation with a general covariant \theta-space sector.