A Lie based 4-dimensional higher Chern-Simons theory

Abstract

We present and study a model of 4-dimensional higher Chern-Simons theory, special Chern-Simons (SCS) theory, instances of which have appeared in the string literature, whose symmetry is encoded in a skeletal semistrict Lie 2-algebra constructed from a compact Lie group with non discrete center. The field content of SCS theory consists of a Lie valued 2-connection coupled to a background closed 3-form. SCS theory enjoys a large gauge and gauge for gauge symmetry organized in an infinite dimensional strict Lie 2-group. The partition function of SCS theory is simply related to that of a topological gauge theory localizing on flat connections with degree 3 second characteristic class determined by the background 3-form. Finally, SCS theory is related to a 3-dimensional special gauge theory whose 2-connection space has a natural symplectic structure with respect to which the 1-gauge transformation action is Hamiltonian, the 2-curvature map acting as moment map.

95 pages, no figures. Discussion of subsection. 3.2 improved. Typo in eq. 2.1.10d corrected

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Cited by in corpus (11)

• $L_{\infty }$-Algebras of Classical Field Theories and the Batalin-Vilkovisky Formalism
• 4-d Chern-Simons Theory: Higher Gauge Symmetry and Holographic Aspects
• Algebraic formulation of higher gauge theory
• Supersymmetric Yang-Mills Theory as Higher Chern-Simons Theory
• Higher Gauge Theory
• Higher Chern-Simons-Antoniadis-Savvidy forms based on crossed modules
• 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
• Quantum field theoretic representation of Wilson surfaces: II higher topological coadjoint orbit model
• Adjusting Higher Chern-Simons Theory