# Super fiber bundles, connection forms, and parallel transport

@inproceedings{Eder2021SuperFB, title={Super fiber bundles, connection forms, and parallel transport}, author={Konstantin Eder}, year={2021} }

The present work provides a mathematically rigorous account on super fiber bundle theory, connection forms and their parallel transport, that ties together various approaches. We begin with a detailed introduction to super fiber bundles. We then introduce the concept of so-called relative supermanifolds as well as bundles and connections defined in these categories. Studying these objects turn out to be of utmost importance in order to, among other things, model anticommuting classical…

## 3 Citations

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

- PhysicsJournal of High Energy Physics
- 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…

### Supergeometry, Supergravity and Kaluza-Klein Theory

- Physics, Geology
- 2022

We discuss methods of consistent Kaluza-Klein truncations of theories of supergravitation. We pay close attention to the underlying gauge and super-gauge theories supporting gravity and supergravity…

### Chiral loop quantum supergravity and black hole entropy

- Physics
- 2022

Recent work has shown that local supersymmetry on a spacetime boundary in N -extended AdS supergravity in chiral variables implies coupling to a boundary OSp( N| 2) C super Chern-Simons theory. We…

## References

SHOWING 1-10 OF 58 REFERENCES

### Super Cartan geometry and the super Ashtekar connection

- Physics
- 2020

This work is devoted to the geometric approach to supergravity. More precisely, we interpret N = 1 supergravity as a super Cartan geometry which provides a link between supergravity and super…

### Super Wilson Loops and Holonomy on Supermanifolds

- Mathematics
- 2013

The classical Wilson loop is the gauge-invariant trace of the parallel transport around a closed path with respect to a connection on a vector bundle over a smooth manifold. We build a precise…

### Infinite-Dimensional Supermanifolds via Multilinear Bundles

- Mathematics
- 2018

In this paper, we provide an accessible introduction to the theory of locally convex supermanifolds in the categorical approach. In this setting, a supermanifold is a functorM : Gr→Man from the…

### Supergravity in the Group‐Geometric Framework: A Primer

- Physics
- 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…

### An invitation to higher gauge theory

- Mathematics
- 2011

In this easy introduction to higher gauge theory, we describe parallel transport for particles and strings in terms of 2-connections on 2-bundles. Just as ordinary gauge theory involves a gauge…

### Pictures from super Chern-Simons theory

- MathematicsJournal of High Energy Physics
- 2020

We study super-Chern-Simons theory on a generic supermanifold. After a self-contained review of integration on supermanifolds, the complexes of forms (superforms, pseudoforms and integral forms) and…

### Supermanifolds: Theory And Applications

- Mathematics
- 2007

This book aims to fill the gap in the literature available on supermanifolds. In two sections, the book describes the different approaches to supermanifolds, with applications to physics, including…

### Global Analytic Approach to Super Teichmueller Spaces

- Mathematics
- 2009

In this thesis we investigate a new formalism for supergeometry which focuses on the categorical properties of the theory. This approach is our main tool in the subsequent investigation of a global…

### Differential cohomology in a cohesive infinity-topos

- Mathematics
- 2013

We formulate differential cohomology and Chern-Weil theory -- the theory of connections on fiber bundles and of gauge fields -- abstractly in the context of a certain class of higher toposes that we…