Integrable (d+1)-dimensional field theories are obtained via homotopy transfer from cyclic L_infinity-algebras describing topological-holomorphic higher Chern-Simons theories on M × CP¹, with integrability encoded in a map to higher Lax connections.
L∞-Algebras of Classical Field Theories and the Batalin-Vilkovisky Formalism
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An algorithm based on homotopy transfer in L∞ algebras produces gauge-invariant fields for massive Kaluza-Klein modes that remain covariant under unbroken zero-mode gauge transformations.
The Poisson bracket in L_infty formulation of field theory is computed via the Peierls formula from the symplectic structure, illustrated in p-adic string theory with a homological algebra interpretation of the inverse relation.
Two inequivalent noncommutative QFTs are built on λ-Minkowski space: a braided version with logarithmic UV divergences and no UV/IR mixing, and a standard version with periodic UV/IR mixing where non-planar correlators are UV-finite but non-analytic at exceptional momenta.
Constructs Čech-de Rham bicomplex from gerbe data for BV-BRST complex and anomaly descent of U(1) 1-form symmetries in Maxwell theory.
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Batalin-Vilkovisky quantization with an angular twist
Two inequivalent noncommutative QFTs are built on λ-Minkowski space: a braided version with logarithmic UV divergences and no UV/IR mixing, and a standard version with periodic UV/IR mixing where non-planar correlators are UV-finite but non-analytic at exceptional momenta.