Super Chern-Simons Theory: BV-formalism and $A_\infty$-algebras

Cremonini, C. A.; Grassi, P. A.

doi:10.48550/arxiv.1912.10807

Cited by 4 publications

(8 citation statements)

References 24 publications

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“…We proceed to discuss the super AKSZ construction, first in the setup without boundary and then in the presence of boundary. We illustrate the construction in the case of super Chern-Simons theory, following [6] and [4]. Afterwards, we discuss in detail the geometric structures present on the superstring worldsheet.…”

Section: Jhep11(2022)160mentioning

confidence: 99%

Super AKSZ construction, integral forms, and the 2-dimensional $$ \mathcal{N} $$ = (1, 1) sigma model

Hulík

Svoboda

Valach

2022

J. High Energ. Phys.

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We discuss a natural extension of the AKSZ construction to the case where the source is given by a supermanifold with a chosen integral form. We then focus on the special case with the target given by a Courant algebroid. In the simplest case this leads to the BV version of the super Chern-Simons theory, as developed by Grassi-Maccaferri and Cremonini-Grassi. In the case of exact Courant algebroids we derive the 2-dimensional $$ \mathcal{N} $$ N = (1, 1) sigma model on the boundary, together with the Wess-Zumino term, paralleling the approach of Ševera in the bosonic case.

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Section: Jhep11(2022)160mentioning

confidence: 99%

Super AKSZ construction, integral forms, and the 2-dimensional $$ \mathcal{N} $$ = (1, 1) sigma model

Hulík

Svoboda

Valach

2022

J. High Energ. Phys.

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“…All the PCO's localize on the same contour, but parametrized by different parameters τ i ∈ T. The definition of the corresponding path-ordering is 12 P Y…”

Section: A Superspace Conventionsmentioning

confidence: 99%

“…Integral forms have been already used to develop a geometric formulation of some simple topological theories such as super Chern-Simons theory [10,11,12] towards d = 3 N = 1 supergravity. In this paper we apply this technique to reformulate supersymmetric Wilson loops in terms of integral forms.…”

mentioning

confidence: 99%

Supersymmetric Wilson loops via integral forms

Cremonini

Grassi

Penati

2020

J. High Energ. Phys.

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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.

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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

Preprint

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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: BV-formalism and $A_\infty$-algebras

Cited by 4 publications

References 24 publications

Super AKSZ construction, integral forms, and the 2-dimensional $$ \mathcal{N} $$ = (1, 1) sigma model

Super AKSZ construction, integral forms, and the 2-dimensional $$ \mathcal{N} $$ = (1, 1) sigma model

Supersymmetric Wilson loops via integral forms

Surface Operators in Superspace

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