Super Chern-Simons theory: Batalin-Vilkovisky formalism and 
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 algebras

Cremonini, C. A.; Grassi, Pietro Antonio

doi:10.1103/physrevd.102.025009

Cited by 11 publications

(13 citation statements)

References 27 publications

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“…In this appendix we recall the main computation techniques for integral forms in the distributional realisation. For a more exhaustive review we suggest [CCGN2] for their introduction in the superalgebraic setting and [CG,CG2,Wit] for their use on supermanifolds.…”

Section: A a Brief Review On Integral Formsmentioning

confidence: 99%

“…The analysis of this example is multi-purposed: first, we give the description complete cohomology for the whole complex of forms; second, we show how pseudoforms arise naturally, at least in this algebraic context. This second result is far from trivial, since despite their recent use in physical contexts (and the formal properties they are supported with) lead to unexpected results (see, e.g., [CGN,CGN2,CCGN,CG,CG2]), their full mathematical understanding is still lacking. In this paper we want to emphasise, at least in an algebraic context, how pseudoforms are strictly related to the existence of sub-superstructures.…”

Section: Introductionmentioning

confidence: 99%

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Cohomology of Lie Superalgebras: Forms, Pseudoforms, and Integral Forms

Cremonini¹,

Grassi²

2021

Preprint

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We study the cohomology of Lie superalgebras for the full complex of forms: superforms, pseudoforms and integral forms. We use the technique of spectral sequences to abstractly compute the Chevalley-Eilenberg cohomology. We first focus on the superalgebra osp(2|2) and show that there exist non-empty cohomology spaces among pseudoforms related to sub-superalgebras. We then extend some classical theorems by Koszul, as to include pseudoforms and integral forms. Further, we conjecture that the algebraic Poincaré duality extends to Lie superalgebras, as long as all the complexes of forms are taken into account and we prove that this holds true for osp(2|2). We finally construct the cohomology representatives explicitly by using a distributional realisation of pseudoforms and integral forms. On one hand, these results show that the cohomology of Lie superalgebras is actually larger than expected, whereas one restricts to superforms only; on the other hand, we show the emergence of completely new cohomology classes represented by pseudoforms. These classes realise as integral form classes of sub-superstructures.

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Section: A a Brief Review On Integral Formsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Cohomology of Lie Superalgebras: Forms, Pseudoforms, and Integral Forms

Cremonini¹,

Grassi²

2021

Preprint

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“…) is invariant under reparametrizations. One has to pay some attention to deal with those "covariant" expressions (in [17], we give a set of rules that indicate how to deal with single delta's).…”

Section: Supervielbeins and The Volume Formmentioning

confidence: 99%

Power to Integral Forms

Cremonini¹,

Grassi²

2021

Preprint

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A novel reformulation of D=4, N=1 supergravity action in the language of integral forms is given. We illustrate the construction of the Berezinian in the supergeometric framework, providing a useful dictionary between mathematics and physics. We present a unified framework for Berezin-Lebesgue integrals for functions and for integral forms. As an application, we discuss Volkov-Akulov theory and its coupling to supergravity from this new perspective.

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“…In this section we briefly review the basics of geometry on supermanifolds and the role of Picture Changing Operators. A more extensive discussion on supergeometry can be found in [64][65][66], whereas applications of this formalism to field theories have been developed in [67][68][69][70][71]. A geometric formulation of (super) Wilson Loops has been recently proposed in [1].…”

Section: Supergeometry and Picture Changing Operatorsmentioning

confidence: 99%

Surface operators in superspace

Cremonini

Grassi

Penati

2020

J. High Energ. Phys.

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We generalize the geometrical formulation of Wilson loops recently introduced in [1] to the description of Wilson Surfaces. For N = (2, 0) theory in six dimensions, we provide an explicit derivation of BPS Wilson Surfaces with non-trivial coupling to scalars, together with their manifestly supersymmetric version. We derive explicit conditions which allow to classify these operators in terms of the number of preserved supercharges. We also discuss kappa-symmetry and prove that BPS conditions in six dimensions arise from kappa-symmetry invariance in eleven dimensions. Finally, we discuss super-Wilson Surfaces — and higher dimensional operators — as objects charged under global p-form (super)symmetries generated by tensorial supercurrents. To this end, the construction of conserved supercurrents in supermanifolds and of the corresponding conserved charges is developed in details.

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Super Chern-Simons theory: Batalin-Vilkovisky formalism and A∞ algebras

Cited by 11 publications

References 27 publications

Cohomology of Lie Superalgebras: Forms, Pseudoforms, and Integral Forms

Cohomology of Lie Superalgebras: Forms, Pseudoforms, and Integral Forms

Power to Integral Forms

Surface operators in superspace

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