Conformal Field Theory and Algebraic Structure of Gauge Theory

Abstract

We consider various homotopy algebras related to Yang-Mills theory and two-dimensional conformal field theory (CFT). Our main objects of study are Yang-Mills $L_{\infty }$ and $C_{\infty }$ algebras and their relation to the certain algebraic structures of Lian-Zuckerman type in CFT. We also consider several examples of algebras related to gauge theory, involving first order formulations and gauge theories with matter fields.

LaTeX2e, 33 pages, minor revisions, typos corrected, published version

References in corpus (13)

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• Perturbed Beta-Gamma Systems and Complex Geometry
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Cited by in corpus (22)

• $L_{\infty }$ Algebras and Field Theory
• Gauge invariant double copy of Yang-Mills theory: the quartic theory
• The Gauge Structure of Double Field Theory follows from Yang-Mills Theory
• $L_{\infty }$ algebras and Tensor Hierarchies in Exceptional Field Theory and Gauged Supergravity
• Scattering amplitudes in YM and GR as minimal model brackets and their recursive characterization
• Tree-Level Color-Kinematics Duality from Pure Spinor Actions
• Quasiclassical Lian-Zuckerman Homotopy Algebras, Courant Algebroids and Gauge Theory
• Homotopy Algebras of Differential (Super)forms in Three and Four Dimensions
• Perturbative Quantum Field Theory and Homotopy Algebras
• A homotopy BV algebra for Yang-Mills and color-kinematics
• Bootstrapping Non-commutative Gauge Theories from L${}_{\infty }$ algebras
• First Order String Theory and the Kodaira-Spencer Equations. I
• Spontaneous symmetry breaking: a view from derived geometry
• HS in flat spacetime. The effective action method
• First Order String Theory and the Kodaira-Spencer Equations. II
• The teleparallel complex
• Worldline quantization of field theory, effective actions and $L_{\infty }$ structure
• Homotopy Relations for Topological VOA
• A-infinity structure in string theory and the Yang-Mills equation
• On higher order Leibniz identities in TCFT
• The $L_{\infty }$-algebra of the S-matrix
• Full S-matrices and Witten diagrams with (relative) L-infinity algebras