All Outputs (64)

Lorentzian bordisms in algebraic quantum field theory (2025)
Journal Article
Bunk, S., MacManus, J., & Schenkel, A. (2025). Lorentzian bordisms in algebraic quantum field theory. Letters in Mathematical Physics, 115, Article 16. https://doi.org/10.1007/s11005-025-01906-3

It is shown that every algebraic quantum field theory has an underlying functorial field theory which is defined on a suitable globally hyperbolic Lorentzian bordism pseudo-category. This means that globally hyperbolic Lorentzian bordisms between Cau... Read More about Lorentzian bordisms in algebraic quantum field theory.

5d 2-Chern-Simons Theory and 3d Integrable Field Theories (2024)
Journal Article
Schenkel, A., & Vicedo, B. (2024). 5d 2-Chern-Simons Theory and 3d Integrable Field Theories. Communications in Mathematical Physics, 405(12), Article 293. https://doi.org/10.1007/s00220-024-05170-9

The 4-dimensional semi-holomorphic Chern-Simons theory of Costello and Yamazaki provides a gauge-theoretic origin for the Lax connection of 2-dimensional integrable field theories. The purpose of this paper is to extend this framework to the setting... Read More about 5d 2-Chern-Simons Theory and 3d Integrable Field Theories.

Universal First-Order Massey Product of a Prefactorization Algebra (2024)
Journal Article
Bruinsma, S., Schenkel, A., & Vicedo, B. (2024). Universal First-Order Massey Product of a Prefactorization Algebra. Communications in Mathematical Physics, 405(9), Article 206. https://doi.org/10.1007/s00220-024-05084-6

This paper studies the universal first-order Massey product of a prefactorization algebra, which encodes higher algebraic operations on the cohomology. Explicit computations of these structures are carried out in the locally constant case, with appli... Read More about Universal First-Order Massey Product of a Prefactorization Algebra.

Quantization of Lorentzian free BV theories: factorization algebra vs algebraic quantum field theory (2024)
Journal Article
Benini, M., Musante, G., & Schenkel, A. (2024). Quantization of Lorentzian free BV theories: factorization algebra vs algebraic quantum field theory. Letters in Mathematical Physics, 114(1), Article 36. https://doi.org/10.1007/s11005-024-01784-1

We construct and compare two alternative quantizations, as a time-orderable prefactorization algebra and as an algebraic quantum field theory valued in cochain complexes, of a natural collection of free BV theories on the category of m-dimensional gl... Read More about Quantization of Lorentzian free BV theories: factorization algebra vs algebraic quantum field theory.

Quantization of derived cotangent stacks and gauge theory on directed graphs (2023)
Journal Article
Benini, M., Pridham, J. P., & Schenkel, A. (2023). Quantization of derived cotangent stacks and gauge theory on directed graphs. Advances in Theoretical and Mathematical Physics, 27(5), 1275-1332. https://doi.org/10.4310/atmp.2023.v27.n5.a1

We study the quantization of the canonical unshifted Poisson structure on the derived cotangent stack T ∗ [X/G] of a quotient stack, where X is a smooth affine scheme with an action of a (reductive) smooth affine group scheme G. This is achieved thro... Read More about Quantization of derived cotangent stacks and gauge theory on directed graphs.

Green Hyperbolic Complexes on Lorentzian Manifolds (2023)
Journal Article
Benini, M., Musante, G., & Schenkel, A. (2023). Green Hyperbolic Complexes on Lorentzian Manifolds. Communications in Mathematical Physics, 403, 699-744. https://doi.org/10.1007/s00220-023-04807-5

We develop a homological generalization of Green hyperbolic operators, called Green hyperbolic complexes, which cover many examples of derived critical loci for gauge-theoretic quadratic action functionals in Lorentzian signature. We define Green hyp... Read More about Green Hyperbolic Complexes on Lorentzian Manifolds.

The Linear CS/WZW Bulk/Boundary System in AQFT (2023)
Journal Article
Benini, M., Grant-Stuart, A., & Schenkel, A. (2024). The Linear CS/WZW Bulk/Boundary System in AQFT. Annales Henri Poincaré, 25, 2251-2294. https://doi.org/10.1007/s00023-023-01346-6

This paper constructs in the framework of algebraic quantum field theory (AQFT) the linear Chern–Simons/Wess–Zumino–Witten system on a class of 3-manifolds M whose boundary ∂M is endowed with a Lorentzian metric. It is proven that this AQFT is equiva... Read More about The Linear CS/WZW Bulk/Boundary System in AQFT.

Strictification theorems for the homotopy time-slice axiom (2023)
Journal Article
Benini, M., Carmona, V., & Schenkel, A. (2023). Strictification theorems for the homotopy time-slice axiom. Letters in Mathematical Physics, 113(1), Article 20. https://doi.org/10.1007/s11005-023-01647-1

It is proven that the homotopy time-slice axiom for many types of algebraic quantum field theories (AQFTs) taking values in chain complexes can be strictified. This includes the cases of Haag–Kastler-type AQFTs on a fixed globally hyperbolic Lorentzi... Read More about Strictification theorems for the homotopy time-slice axiom.

BV quantization of dynamical fuzzy spectral triples (2022)
Journal Article
Gaunt, J., Nguyen, H., & Schenkel, A. (2022). BV quantization of dynamical fuzzy spectral triples. Journal of Physics A: Mathematical and Theoretical, 55(47), Article 474004. https://doi.org/10.1088/1751-8121/aca44f

This paper provides a systematic study of gauge symmetries in the dynamical fuzzy spectral triple models for quantum gravity that have been proposed by Barrett and collaborators. We develop both the classical and the perturbative quantum BV formalism... Read More about BV quantization of dynamical fuzzy spectral triples.

A Skeletal Model for 2d Conformal AQFTs (2022)
Journal Article
Benini, M., Giorgetti, L., & Schenkel, A. (2022). A Skeletal Model for 2d Conformal AQFTs. Communications in Mathematical Physics, 395(1), 269-298. https://doi.org/10.1007/s00220-022-04428-4

A simple model for the localization of the category CLoc2 of oriented and time-oriented globally hyperbolic conformal Lorentzian 2-manifolds at all Cauchy morphisms is constructed. This provides an equivalent description of 2-dimensional conformal al... Read More about A Skeletal Model for 2d Conformal AQFTs.

Relative Cauchy Evolution for Linear Homotopy AQFTs (2022)
Journal Article
Bruinsma, S., Fewster, C. J., & Schenkel, A. (2022). Relative Cauchy Evolution for Linear Homotopy AQFTs. Communications in Mathematical Physics, 392(2), 621-657. https://doi.org/10.1007/s00220-022-04352-7

This paper develops a concept of relative Cauchy evolution for the class of homotopy algebraic quantum field theories (AQFTs) that are obtained by canonical commutation relation quantization of Poisson chain complexes. The key element of the construc... Read More about Relative Cauchy Evolution for Linear Homotopy AQFTs.

Homotopical Analysis of 4d Chern-Simons Theory and Integrable Field Theories (2022)
Journal Article
Benini, M., Schenkel, A., & Vicedo, B. (2022). Homotopical Analysis of 4d Chern-Simons Theory and Integrable Field Theories. Communications in Mathematical Physics, 389, 1417-1443. https://doi.org/10.1007/s00220-021-04304-7

This paper provides a detailed study of 4-dimensional Chern-Simons theory on R2× CP1 for an arbitrary meromorphic 1-form ω on CP1. Using techniques from homotopy theory, the behaviour under finite gauge transformations of a suitably regularised versi... Read More about Homotopical Analysis of 4d Chern-Simons Theory and Integrable Field Theories.

Smooth 1-Dimensional Algebraic Quantum Field Theories (2021)
Journal Article
Benini, M., Perin, M., & Schenkel, A. (2022). Smooth 1-Dimensional Algebraic Quantum Field Theories. Annales Henri Poincaré, 23, 2069-2111. https://doi.org/10.1007/s00023-021-01132-2

This paper proposes a refinement of the usual concept of algebraic quantum field theories (AQFTs) to theories that are smooth in the sense that they assign to every smooth family of spacetimes a smooth family of observable algebras. Using stacks of c... Read More about Smooth 1-Dimensional Algebraic Quantum Field Theories.

Batalin–Vilkovisky quantization of fuzzy field theories (2021)
Journal Article
Nguyen, H., Schenkel, A., & Szabo, R. J. (2021). Batalin–Vilkovisky quantization of fuzzy field theories. Letters in Mathematical Physics, 111(6), Article 149. https://doi.org/10.1007/s11005-021-01490-2

We apply the modern Batalin–Vilkovisky quantization techniques of Costello and Gwilliam to noncommutative field theories in the finite-dimensional case of fuzzy spaces. We further develop a generalization of this framework to theories that are equiva... Read More about Batalin–Vilkovisky quantization of fuzzy field theories.

Classical BV formalism for group actions (2021)
Journal Article
Benini, M., Safronov, P., & Schenkel, A. (2023). Classical BV formalism for group actions. Communications in Contemporary Mathematics, 25(1), Article 2150094. https://doi.org/10.1142/S0219199721500942

We study the derived critical locus of a function f: [X/G] → 1 on the quotient stack of a smooth affine scheme X by the action of a smooth affine group scheme G. It is shown that dCrit(f) R [Z/G] is a derived quotient stack for a derived affine schem... Read More about Classical BV formalism for group actions.

Categorification of algebraic quantum field theories (2021)
Journal Article
Benini, M., Perin, M., Schenkel, A., & Woike, L. (2021). Categorification of algebraic quantum field theories. Letters in Mathematical Physics, 111(2), Article 35. https://doi.org/10.1007/s11005-021-01371-8

This paper develops a concept of 2-categorical algebraic quantum field theories (2AQFTs) that assign locally presentable linear categories to spacetimes. It is proven that ordinary AQFTs embed as a coreflective full 2-subcategory into the 2-category... Read More about Categorification of algebraic quantum field theories.

Dirac operators on noncommutative hypersurfaces (2020)
Journal Article
Nguyen, H., & Schenkel, A. (2020). Dirac operators on noncommutative hypersurfaces. Journal of Geometry and Physics, 158, Article 103917. https://doi.org/10.1016/j.geomphys.2020.103917

© 2020 Elsevier B.V. This paper studies geometric structures on noncommutative hypersurfaces within a module-theoretic approach to noncommutative Riemannian (spin) geometry. A construction to induce differential, Riemannian and spinorial structures f... Read More about Dirac operators on noncommutative hypersurfaces.

Operads for algebraic quantum field theory (2020)
Journal Article
Benini, M., Schenkel, A., & Woike, L. (2021). Operads for algebraic quantum field theory. Communications in Contemporary Mathematics, 23(2), Article 2050007. https://doi.org/10.1142/S0219199720500078

We construct a colored operad whose category of algebras is the category of algebraic quantum field theories. This is achieved by a construction that depends on the choice of a category, whose objects provide the operad colors, equipped with an addit... Read More about Operads for algebraic quantum field theory.

On the relationship between classical and deformed Hopf fibrations (2020)
Journal Article
Brzeziński, T., Gaunt, J., & Schenkel, A. (2020). On the relationship between classical and deformed Hopf fibrations. Symmetry, Integrability and Geometry: Methods and Applications, 16, Article 008. https://doi.org/10.3842/sigma.2020.008

The θ-deformed Hopf fibration S3θ→S2 over the commutative 2-sphere is compared with its classical counterpart. It is shown that there exists a natural isomorphism between the corresponding associated module functors and that the affine spaces of clas... Read More about On the relationship between classical and deformed Hopf fibrations.

Homological perspective on edge modes in linear Yang–Mills and Chern–Simons theory (2020)
Journal Article
Mathieu, P., Murray, L., Schenkel, A., & Teh, N. J. (2020). Homological perspective on edge modes in linear Yang–Mills and Chern–Simons theory. Letters in Mathematical Physics, 110, 1559–1584. https://doi.org/10.1007/s11005-020-01269-x

We provide an elegant homological construction of the extended phase space for linear Yang-Mills theory on an oriented and time-oriented Lorentzian manifold M with a time-like boundary @M that was proposed by Donnelly and Freidel [JHEP 1609, 102 (201... Read More about Homological perspective on edge modes in linear Yang–Mills and Chern–Simons theory.