Superstring field theory, superforms and supergeometry

We study super-Chern-Simons theory on a generic supermanifold. After a self-contained review of integration on supermanifolds, the complexes of forms (superforms, pseudo-forms and integral forms) and the extended Cartan calculus are discussed. We then introduce Picture Changing Operators. We provide several examples of computation of PCO's acting on different type of forms. We illustrate also the action of the η operator, crucial ingredient to define the interactions of super Chern-Simons theory. Then, we discuss the action for super Chern-Simons theory on any supermanifold, first in the factorized form (3-form × PCO) and then, we consider the most general expression. The latter is written in term of psuedo-forms containing an infinite number of components. We show that the free equations of motion reduce to the usual Chern-Simons equations yielding the proof of the equivalence between the formulations at different pictures of the same theory. Finally, we discuss the interaction terms. They require a suitable definition in order to take into account the picture number. That implies the construction of a 2-product which is not associative that inherits an A ∞ algebra structure. That shares several similarities with a recent construction of a super string field theory action by

“…an expression containing negative powers of dθ. We remark, as was discussed in [19], that the introduction of inverse form requires the definition of a new complex Ω…”

Section: Geometric Picture Changing Operators: Some Explicit Resultsmentioning

confidence: 79%

Section: Bibliography 54mentioning

confidence: 85%

Section: Geometric Picture Changing Operators: Some Explicit Resultsmentioning

confidence: 99%

Section: Bibliography 54mentioning

confidence: 99%

See 2 more Smart Citations

Pictures from super Chern-Simons theory

Cremonini

Grassi

2020

“…Here we follow the strategy pioneered by Belopolsky [2], where integral forms are distributional-like forms on which a suitable Cartan calculus can be developed. We clarify the basic ingredients and rules, and refer to the literature [1,11,34,35] for a complete description.…”

Section: Superdifferential Formsmentioning

confidence: 99%

Supersymmetric Wilson loops via integral forms

Cremonini

Grassi

Penati

2020

We study supersymmetric Wilson loops from a geometrical perspective. To this end, we propose a new formulation of these operators in terms of an integral form associated to the immersion of the loop into a supermanifold. This approach provides a unifying description of Wilson loops preserving different sets of supercharges, and clarifies the flow between them. Moreover, it allows to exploit the powerful techniques of super-differential calculus for investigating their symmetries.As remarkable examples, we discuss supersymmetry and kappa-symmetry invariance.

Holst-MacDowell-Mansouri action for (extended) supergravity with boundaries and super Chern-Simons theory

Eder

Sahlmann

2021

In this article, the Cartan geometric approach toward (extended) supergravity in the presence of boundaries will be discussed. In particular, based on new developments in this field, we will derive the Holst variant of the MacDowell-Mansouri action for $$ \mathcal{N} $$ N = 1 and $$ \mathcal{N} $$ N = 2 pure AdS supergravity in D = 4 for arbitrary Barbero-Immirzi parameters. This action turns out to play a crucial role in context of boundaries in the framework of supergravity if one imposes supersymmetry invariance at the boundary. For the $$ \mathcal{N} $$ N = 2 case, it follows that this amounts to the introduction of a θ-topological term to the Yang-Mills sector which explicitly depends on the Barbero-Immirzi parameter. This shows the close connection between this parameter and the θ-ambiguity of gauge theory.We will also discuss the chiral limit of the theory, which turns out to possess some very special properties such as the manifest invariance of the resulting action under an enlarged gauge symmetry. Moreover, we will show that demanding supersymmetry invariance at the boundary yields a unique boundary term corresponding to a super Chern-Simons theory with OSp($$ \mathcal{N} $$ N |2) gauge group. In this context, we will also derive boundary conditions that couple boundary and bulk degrees of freedom and show equivalence to the results found in the D’Auria-Fré approach in context of the non-chiral theory. These results provide a step towards of quantum description of supersymmetric black holes in the framework of loop quantum gravity.