Higher Chern-Simons based on (2-)crossed modules

Song, Danhua; Wu, Mengyao; Wu, Ke; Yang, Jie

doi:10.1007/jhep07(2023)207

J. High Energ. Phys.

2023

DOI: 10.1007/jhep07(2023)207

|View full text |Cite

Higher Chern-Simons based on (2-)crossed modules

Danhua Song

Mengyao Wu

Ke Wu

et al.

Abstract: We present higher Chern-Simons theories based on (2-)crossed modules. We start from the generalized differential forms in Generalized Differential Calculus and define the corresponding generalized connections which consist of higher connections. Then we establish the generalized Chern-Simons forms to get the higher Chern-Simons actions. Finally, we develop the higher second Chern forms and Chern-Weil theorems.

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2024

Publication Types

Select...

Article1

Relationship

Self Cite0

Independent1

Authors

Journals

Cited by 1 publication

References 60 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

Higher gauge theory and integrability

Chen,

Liniado

2024

Phys. Rev. D

View full text Add to dashboard Cite

In recent years, significant progress has been made in the study of integrable systems from a gauge theoretic perspective. This development originated with the introduction of four-dimensional Chern-Simons theory with defects, which provided a systematic framework for constructing two-dimensional integrable systems. In this article, we propose a novel approach to studying higher-dimensional integrable models employing techniques from higher category theory. Starting with higher Chern-Simons theory on the 4-manifold R×Y, we complexify and compactify the real line to CP1 and introduce the disorder defect ω=z−1dz. This procedure defines a holomorphic five-dimensional variant of higher Chern-Simons theory, which, when endowed with suitable boundary conditions, allows for the localization to a three-dimensional theory on Y. The equations of motion of the resulting model are equivalent to the flatness of a 2-connection (L,H), that we then use to construct the corresponding higher holonomies. We prove that these are invariants of homotopies relative boundary, which enables the construction of conserved quantities. The latter are labeled by both the categorical characters of a Lie crossed module and the infinite number of homotopy classes of surfaces relative boundary in Y. Moreover, we also demonstrate that the three-dimensional theory has left and right acting symmetries whose current algebra is given by an infinite-dimensional centrally extended affine Lie 2-algebra. Both of these conditions are direct higher homotopy analogs of the properties satisfied by the two-dimensional Wess-Zumino-Witten conformal field theory, which we therefore interpret as facets of integrable structures. Published by the American Physical Society 2024

show abstract

Higher gauge theory and integrability

Chen,

Liniado

2024

Phys. Rev. D

View full text Add to dashboard Cite

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Higher Chern-Simons based on (2-)crossed modules

Cited by 1 publication

References 60 publications

Higher gauge theory and integrability

Higher gauge theory and integrability

Contact Info

Product

Resources

About