Super-Quantum Mechanics in the Integral Form Formalism

Fortschritte der Physik

2018

We review the group‐geometric approach to supergravity theories, in the perspective of recent developments and applications. Usual diffeomorphisms, gauge symmetries and supersymmetries are unified as superdiffeomorphisms in a supergroup manifold. Integration on supermanifolds is briefly revisited, and used as a tool to provide a bridge between component and superspace actions. As an illustration of the constructive techniques, the cases of d=3,4 off‐shell supergravities and d=5 Chern‐Simons supergravity are discussed in detail. A cursory account of d=10+2 supergravity is also included. We recall a covariant canonical formalism, well adapted to theories described by Lagrangians d‐forms, that allows to define a form hamiltonian and to recast constrained hamiltonian systems in a covariant form language. Finally, group geometry and properties of spinors and gamma matrices in d=s+t dimensions are summarized in Appendices.

Section: Doi: 101002/prop201800014mentioning

confidence: 99%

“…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.…”

Section: Appendix A: Group Manifold Geometrymentioning

confidence: 99%

Supergravity in the Group‐Geometric Framework: A Primer

Fortschritte der Physik

2018

“…where the Lagrangian L (n|0) is a superfield (n|0) superform and Y (0|m) is a Picture Changing Operator (PCO), or using a proper mathematical identification (see for ex. [7]), is the Poincaré dual form of the embedding of a n-dimensional bosonic submanifold into the supermanifold M (n|m) . Y (0|m) belongs to the super de Rham cohomology H (0|m) (M (n|m) ).…”

Section: Introductionmentioning

confidence: 99%

“…In particular, we will study the case N = 1 and N = 2. The cases D = 1, D = 2 and D = 3 are treated in [7], [8], [9].…”

Section: Introductionmentioning

confidence: 99%

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

Catenacci

Grassi

2018

J. High Energ. Phys.

Self Cite

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.

“…[1][2][3]). Recent advances in superintegration theory [4][5][6][7] have shown how this approach interpolates between superspace and component actions.…”

Section: Introductionmentioning

confidence: 99%

Gauge supergravity in D = 2 + 2

2017

J. High Energ. Phys.

We present an action for chiral N = (1, 0) supergravity in 2 + 2 dimensions. The fields of the theory are organized into an OSp(1|4) connection supermatrix, and are given by the usual vierbein V a , spin connection ω ab , and Majorana gravitino ψ. In analogy with a construction used for D = 10 + 2 gauge supergravity, the action is given by STr(R 2 Γ), where R is the OSp(1|4) curvature supermatrix two-form, and Γ a constant supermatrix containing γ 5 . It is similar, but not identical to the MacDowell-Mansouri action for D = 2 + 2 supergravity. The constant supermatrix breaks OSp(1|4) gauge invariance to a subalgebra OSp(1|2) ⊕ Sp(2), including a Majorana-Weyl supercharge. Thus half of the OSp(1|4) gauge supersymmetry survives. The gauge fields are the selfdual part of ω ab and the Weyl projection of ψ for OSp(1|2), and the antiselfdual part of ω ab for Sp(2). Supersymmetry transformations, being part of a gauge superalgebra, close off-shell. The selfduality condition on the spin connection can be consistently imposed, and the resulting "projected" action is OSp(1|2) gauge invariant.