4-d semistrict higher Chern-Simons theory I

Abstract

We formulate a 4-dimensional higher gauge theoretic Chern-Simons theory. Its symmetry is encoded in a semistrict Lie 2-algebra equipped with an invariant non singular bilinear form. We analyze the gauge invariance of the theory and show that action is invariant under a higher gauge transformation up to a higher winding number. We find that the theory admits two seemingly inequivalent canonical quantizations. The first is manifestly topological, it does not require a choice of any additional structure on the spacial 3-fold. The second, more akin to that of ordinary Chern-Simons theory, involves fixing a CR structure on the latter. Correspondingly, we obtain two sets of semistrict higher WZW Ward identities and we find the explicit expressions of two higher versions of the WZW action. We speculate that the model could be used to define 2-knot invariants of 4-folds.

97 pages, LaTex, a few references added

References in corpus (7)

• The Geometry of the Master Equation and Topological Quantum Field Theory
• Introduction to sh Lie algebras for physicists
• An Invitation to Higher Gauge Theory
• Čech cocycles for differential characteristic classes -- An infinity-Lie theoretic construction
• L-infinity algebra connections and applications to String- and Chern-Simons n-transport
• A higher Chern-Weil derivation of AKSZ sigma-models
• Lie 2-algebra models

Cited by in corpus (19)

• $L_{\infty }$-Algebras of Classical Field Theories and the Batalin-Vilkovisky Formalism
• A new formulation of higher parallel transport in higher gauge theory
• Higher Groupoid Bundles, Higher Spaces, and Self-Dual Tensor Field Equations
• 4-d Chern-Simons Theory: Higher Gauge Symmetry and Holographic Aspects
• A Lie based 4-dimensional higher Chern-Simons theory
• Generalized Higher Gauge Theory
• Algebraic formulation of higher gauge theory
• Supersymmetric Yang-Mills Theory as Higher Chern-Simons Theory
• On higher holonomy invariants in higher gauge theory I
• On higher holonomy invariants in higher gauge theory II
• Higher Gauge Theory
• Higher Chern-Simons-Antoniadis-Savvidy forms based on crossed modules
• Higher Gauge Theory and Integrability
• Higher Chern-Simons based on (2-)crossed modules
• Extended Cartan homotopy formula for higher Chern-Simons-Antoniadis-Savvidy theory
• Quantum field theoretic representation of Wilson surfaces: I higher coadjoint orbit theory
• Higher (gauged) Wess--Zumino--Witten terms based on Lie crossed modules
• Quantum field theoretic representation of Wilson surfaces: II higher topological coadjoint orbit model
• Adjusting Higher Chern-Simons Theory