Wess-Zumino and super Yang-Mills theories in D=4 integral superspace

Abstract

We reconstruct the action of N = 1, D = 4 Wess-Zumino and N = 1, 2, D = 4 super-Yang-Mills theories, using integral top forms on the supermanifold M (4|4) . Choosing different Picture Changing Operators, we show the equivalence of their rheonomic and superspace actions. The corresponding supergeometry and integration theory are discussed in detail. This formalism is an efficient tool for building supersymmetric models in a geometrical framework.

Supergravity in the Group‐Geometric Framework: A Primer

“…[9] for a recent review, or [10] for a textbook), and new developments concerning integral forms, discussed in refs. [11][12][13][14][15]. Section 5 summarizes the building rules of d-form Lagrangians, applied in subsequent examples.…”

“…For infinitesimal x: 14 Hereafter G indicates the part of the group connected with the identity. 15 Since G is a Lie group, this function is smooth. so that the t A are a differential representation of the abstract generators T A , and satisfy therefore the same algebra:…”

“…The Lie-valued one-form σ (y) can also be constructed directly from the group element y: 15) It is easy to verify that (A.15) satisfies the Cartan-Maurer equation (A.14) (use dy −1 = −y −1 dy y −1 ). Moreover, it takes the same value as e A M dy M T A at the origin y = 0.…”

Chern-Simons supergravity on supergroup manifolds

“…and η M 3 is the Poincaré dual of the 3-dimensional Minkowski space M 3 immersed into the superspace M (3|2) (see e.g. [12][13][14][15]). η M 3 is a 2-form in superspace 1 that after integration localizes the Lagrangian on the d = 3 bosonic subspace, i.e.…”

“…Promoting both A a and ψ α to (1|0)superforms (for a discussion on forms on supermanifolds see e.g. [12][13][14][15]), they read…”