Minimal models of field theories: SDYM and SDGR

Abstract

There exists a natural $L_{\infty }$-algebra or $Q$-manifold that can be associated to any (gauge) field theory. Perturbatively, it can be obtained by reducing the $L_{\infty }$-algebra behind the jet space BV-BRST formulation to its minimal model. We explicitly construct the minimal models of self-dual Yang-Mills and self-dual gravity theories, which also represents their equations of motion as Free Differential Algebras. The minimal model regains all relevant information about the field theory, e.g. actions, charges, anomalies, can be understood in terms of the corresponding $Q$-cohomology.

arXiv comment23 pages + Appendices + Refs = 40 pages

References in corpus (38)

• New Relations for Gauge-Theory Amplitudes
• Perturbative Gauge Theory As A String Theory In Twistor Space
• Perturbative Quantum Gravity as a Double Copy of Gauge Theory
• Closed String Field Theory: Quantum Action and the BV Master Equation
• Introduction to string field theory
• The Geometry of the Master Equation and Topological Quantum Field Theory
• Introduction to sh Lie algebras for physicists
• Local BRST cohomology in the antifield formalism: I. General theorems
• Conformal Supergravity in Twistor-String Theory
• The self-dual sector of QCD amplitudes
• Tensor Constructions of Open String Theories I: Foundations
• Light-Front Higher-Spin Theories in Flat Space
• $L_{\infty }$ Algebras and Field Theory
• Local BRST cohomology in the antifield formalism: II. Application to Yang-Mills theory
• Quantum Chiral Higher Spin Gravity
• Parent field theory and unfolding in BRST first-quantized terms
• Higher Spin Interactions in Four Dimensions: Vasiliev vs. Fronsdal
• Local BRST cohomology and covariance
• $L_{\infty }$-Algebras of Classical Field Theories and the Batalin-Vilkovisky Formalism
• Noncommutative homotopy algebras associated with open strings
• Chiral Higher Spin Theories and Self-Duality
• More on Quantum Chiral Higher Spin Gravity
• Self-Dual N=8 Supergravity as Closed N=2(4) Strings
• Actions for Self-dual Higher Spin Gravities
• Double Copy from Homotopy Algebras
• A double copy for asymptotic symmetries in the self-dual sector
• On matter-free Higher Spin Gravities in 3d: (partially)-massless fields and general structure
• A Poincare lemma for sigma models of AKSZ type
• Self-Dual Gravity
• First order parent formulation for generic gauge field theories
• One-loop Finiteness of Chiral Higher Spin Gravity
• Parent formulations, frame-like Lagrangians, and generalized auxiliary fields
• Frame-like Lagrangians and presymplectic AKSZ-type sigma models
• Flat Self-dual Gravity
• Gauge PDE and AKSZ-type Sigma Models
• Characteristic Cohomology and Observables in Higher Spin Gravity
• Higher Spin Gravities and Presymplectic AKSZ Models
• A Chiral Perturbation Expansion for Gravity

Cited by in corpus (4)

• Radiative phase space extensions at all orders in r for self-dual Yang-Mills and Gravity
• Minimal model of Chiral Higher Spin Gravity
• Chiral Higher Spin Gravity and Convex Geometry
• Massless chiral fields in six dimensions