arXiv subjects

Leron Borsten

Publications and source records attributed to Leron Borsten.

At least 19 recordsLinked to original sources

arXiv2026

Higher-order analogues of colour-kinematics duality in first-order Yang-Mills Feynman diagrams

Colour-kinematics duality is, even at tree level, not manifest from the standard Lagrangian of Yang-Mills theory in that the usual Feynman-diagram expansion does not follow the kinematic Jacobi identities. For a Lagrangian manifesting colour-kinematics duality, the kinematic Jacobi identities of the Feynman-diagram expansion follow from the existence of a second-order differential operator $\mathsf{b}$ acting on the algebra of colour-stripped fields that forms part of the data of a BV$^\square$-algebra. We argue that the existence of differential operators of order greater than two implies weaker but nontrivial fragments of kinematic Jacobi identities. We further show that a superspace formulation of the first-order Yang-Mills action in the Batalin-Vilkovisky formalism admits a differential operator of order six in every spacetime dimension. Therefore, the Feynman-diagram expansion of tree and loop scattering amplitudes of the first-order formulation of Yang-Mills theory automatically enjoy a weak form of colour-kinematics duality.

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arXiv2026

Limits to Computational Acceleration Imposed by Quantum Field Theory and Quantum Gravity

A computer, in order to perform a given computation, requires a certain amount of space (memory) and a certain amount of time (runtime). This leaves certain computations beyond reach due to technological limits on processing speed and memory density. Some computations, such as the halting problem, are not possible even in principle. However, curved spacetimes and exotic fields appear to provide avenues to accelerate computation, for instance by exploiting time dilation. Impossible computations seemingly become tractable, butting up against intuition. However, we show that such schemes are consistently thwarted by physical effects from quantum gravity (including swampland conjectures) and quantum field theory in curved space. More precisely, we show that an observer and a computer able to withstand energy scales up to order $E$ can, by using relativistic effects, accelerate computation at a rate of at most $\mathcal O(1)E$ e-folds per unit time in natural units: $(\ln\alpha)/\tau\lesssim E$. The Bekenstein bound for entropy can then be understood as the space (memory) analogue to (run)time: if a computer of length scale $D$, operating at energies up to order $E$, has access to $N$ different memory states, then $(\ln N)/D\lesssim E$.

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arXiv2026

Integrability from Homotopy Algebras

Homotopy algebraic methods have become increasingly influential in studying field theories. We consider semi-holomorphic Chern-Simons theory and its relation with the principal chiral model. In particular, we establish an explicit quasi-isomorphism between the cyclic $L_\infty$-algebras governing both theories which directly gives the Lax connection. This provides a concrete example for studying integrability of a two-dimensional system through the homotopy algebraic lens.

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arXiv2026

Ersatz gravity and black-hole thermodynamics from Manin gauge theory with noncompact gauge group

We show that a three-dimensional Manin gauge theory with gauge group $\operatorname{SL}(2;\mathbb R)$ (i.e. Yang-Mills theory, the third-way theory, or the imaginary third-way theory) minimally coupled to Einstein gravity admits a dual interpretation as Einstein gravity with an exotic coupling to a Manin gauge theory, where the roles of dreibein/spin connection and field strength/gauge potential are interchanged. The dual, or ersatz, gravitational metric $\hat g_{\mu\nu}\sim\operatorname{tr}((\star F)_\mu (\star F)_\nu)$ is a classical double copy of the gauge field strength $F_{\mu\nu}$ (as opposed to the usual double copy of the gauge potential $A_\mu$). If matter exclusively couples to $\hat g$ (for example, in a gravitational decoupling limit), then one can formulate black-hole thermodynamics with regards to the ersatz metric. In particular, a black-hole solution for the ersatz metric $\hat g_{\mu\nu}$ (made of Yang-Mills fields) radiates ersatz Hawking radiation and obeys the laws of black-hole thermodynamics.

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arXiv2025

Discrete Approximations to $\operatorname{U}(1)$ Principal Bundles in Abelian Gauge Theory

A $(d+1)$-dimensional field theory with a periodic spatial dimension may be approximated by a $d$-dimensional theory with a truncated Kaluza-Klein tower of $k$ fields; as ${k\to\infty}$, one recovers the original $(d+1)$-dimensional theory. One may similarly expect that $\operatorname{U}(1)$-valued Maxwell theory may be approximated by $\mathbb Z_k$-valued gauge theory and that, as $k\to\infty$, one recovers the original Maxwell theory. However, this fails: the ${k\to\infty}$ limit of $\mathbb Z_k$-valued gauge theory is flat Maxwell theory with no local degrees of freedom. We instead construct field theories $\mathcal T_k$ such that, with appropriate matter couplings, the $k\to\infty$ limit does recover Maxwell theory in the absence of magnetic monopoles (but with possible Wilson loops), and show that $\mathcal T_k$ can be understood as Maxwell theory with the insertion of a certain nonlocal operator that projects out principal $\operatorname{U}(1)$-bundles that do not arise from principal $\mathbb Z_k$-bundles sectors (in particular, projecting out sectors with monopole charges).

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arXiv2025

Brane Symmetries Revisited: Symmetries of Tensile and Tensionless Branes in Possibly Degenerate Metrics and their Manifestations

We analyse the symmetries of tensionless and tensile branes moving in a target space with a possibly degenerate metric, with the worldvolume metric remaining nondegenerate. We recover known results about symmetries of strings and branes as well as new results in the tensionless and degenerate-metric cases. We comment on ramifications in the corresponding bulk theories.

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arXiv2025

Localisation with on-shell supersymmetry algebras via the Batalin-Vilkovisky formalism: Localisation as gauge fixing

The Batalin-Vilkovisky formalism provides a powerful technique to deal with gauge and global (super)symmetries that may only hold on shell. We argue that, since global (super)symmetries and gauge symmetries appear on an equal footing in the Batalin-Vilkovisky formalism, similarly localisation with respect to global (super)symmetries appears on an equal footing with gauge fixing of gauge symmetries; in general, when the gauge-fixing condition is not invariant under the global symmetries, localisation (with respect to a localising fermion) and gauge fixing (with respect to a gauge-fixing fermion) combine into a single operation. Furthermore, this perspective enables supersymmetric localisation using only on-shell supermultiplets, dispensing with auxiliary fields, extending an insight first discovered by Losev and Lysov arXiv:2312.13999. We provide the first examples of on-shell localisation for quantum field theories (together with a companion paper by Arvanitakis arXiv:2511.00144).

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arXiv2025

Symmetries Beget Symmetries: Ghostly Higher-Form Symmetries and the Descent Equation

Viewed through the lens of the Batalin-Vilkovisky formalism, we demonstrate that higher-form currents with nonzero ghost number also define higher-form symmetries, directly analogous to the standard higher-form symmetries with ghost number zero. These ghostly higher symmetries descend from and into conventional higher-form symmetries via chains of descent equations familiar from the theory of anomalies and topological field theories. We give examples of such chains of ghostly symmetries in Maxwell theory, Abelian and non-Abelian higher gauge theory, Yang-Mills theory, and beyond.

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arXiv2025

Sandwich Construction of Symmetry TFTs for the Centre Symmetries of Chern-Simons, Yang-Mills, and Einstein Gravity

We construct symmetry topological field theories (SymTFTs) using the sandwich construction of Pulmann-\v{S}evera-Valach that manifest the centre symmetries of Chern-Simons theory and Yang-Mills theory as well as general relativity in the MacDowell-Mansouri formulation. The 'filling' of the sandwich is an AKSZ sigma model whose target space is a Weil algebra, augmented with discrete degrees of freedom given by a choice of topological boundary condition.

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arXiv2025

Twisted Homotopy Algebras: Supersymmetric Twists, Spontaneous Symmetry Breaking, Anomalies and Localisation

Twisting and classical background fields are two foundational techniques in supersymmetric quantum field theory, central to developments ranging from the Higgs mechanism to topological twisting and supersymmetric localisation. While traditionally treated as distinct procedures, they appear on an equal footing in the homotopy-algebraic approach to quantum field theory. In this work, we formalise this connection by interpreting both twisting and the introduction of classical backgrounds as instances of twisting curved quantum $L_\infty$-superalgebras. Using the language of homotopy algebras and the Batalin-Vilkovisky formalism, we provide a unified algebraic framework that encompasses topological/holomorphic twists, spontaneous symmetry breaking, computation of anomalies, and supersymmetric localisation \`a la Festuccia--Seiberg. As a byproduct, we introduce a notion of twisting for quantum $L_\infty$-algebras and a homotopy-algebraic reformulation of the one-particle-irreducible effective action.

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arXiv2025

Discrete $p$-Form Symmetry and Higher Coulomb Phases

We argue that a field theory with a $\mathbb Z_N$ $p$-form symmetry generically admits, in addition to a Higgs phase and a 'confining' phase, a Coulomb phase in which the infrared theory contains Abelian $p$-form electrodynamics, similar to the behaviour of Yang-Mills theory coupled to adjoint or fundamental matter. We illustrate our claim with continuum and lattice examples.

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arXiv2025

Duality Anomalies in Linearized Gravity

Classical linearized gravity admits a dual formulation in terms of a higher-rank tensor field. Proposing a prescription for the instanton sectors of linearized gravity and its dual, we show that they may be quantum inequivalent in even dimensions. The duality anomaly is obtained by resolving the dual graviton theories into vector-valued $p$-form electrodynamics and is controlled by the Reidemeister torsion, Ray-Singer torsion and Euler characteristic of the cotangent bundle. Under the proposed instanton prescription the duality anomaly vanishes for an odd number of spacetime dimensions as a consequence of the celebrated Cheeger-M\"uller theorem. In the presence of a gravitational $\theta$-term, the partition function is a modular form in direct analogy to Abelian S-duality for Maxwell theory.

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arXiv2025

Homotopy Manin Theories: Generalising Third-Way, Yang-Mills and Integrable Sigma Models

Manin theories are a class of non-topological deformations of Chern-Simons theories that naturally realise the third-way mechanism and furthermore admit localisation despite not being supersymmetric in the usual sense. In this paper, we extend this construction to higher dimensions, thereby producing a large class of examples of third-way-type theories. Furthermore, the construction naturally yields Yang-Baxter integrable deformations of the principal chiral model as well as gravitational models various dimensions.

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arXiv2024

Full S-matrices and Witten diagrams with (relative) L-infinity algebras

The $L_\infty$-algebra approach to scattering amplitudes elegantly describes the nontrivial part of the $S$-matrix but fails to take into account the trivial part. We argue that the trivial contribution to the $S$-matrix should be accounted for by another, complementary $L_\infty$-algebra, such that a perturbative field theory is described by a cyclic relative $L_\infty$-algebra. We further demonstrate that this construction reproduces Witten diagrams that arise in AdS/CFT including, in particular, the trivial Witten diagrams corresponding to CFT two-point functions. We also discuss Chern-Simons theory and Yang-Mills theory on manifolds with boundaries using this approach.

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arXiv2024

Gravity from AKSZ-Manin theories in two, three, and four dimensions

We show that various dynamical gauge theories in two, three and four dimensions, obtained as Manin deformations of topological Alexandrov-Kontsevich-Schwarz-Zaboronsky (AKSZ) theories, are equivalent to gravitational theories. Since gravity is topological in two and three dimension, this equivalence requires a diffeomorphism breaking background source term. In four dimensions, however, the MacDowell-Mansouri formulation of Einstein gravity with a cosmological constant is obtained identically via the Manin deformation of a particular AKSZ theory.

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arXiv2024

Ambitwistor Yang-Mills Theory Revisited

Inspired by the Movshev-Mason-Skinner Cauchy-Riemann (CR) ambitwistor approach, we provide a rigorous yet elementary construction of a twisted CR holomorphic Chern-Simons action on CR ambitwistor space for maximally supersymmetric Yang-Mills theory on four-dimensional Euclidean space. The key ingredient in our discussion is the homotopy algebraic perspective on perturbative quantum field theory. Using this technology, we show that both theories are semi-classically equivalent, that is, we construct a quasi-isomorphism between the cyclic $L_\infty$-algebras governing both field theories. This confirms a conjecture from the literature. Furthermore, we also show that the Yang-Mills action is obtained by integrating out an infinite tower of auxiliary fields in the Chern-Simons action, that is, the two theories are related by homotopy transfer. Given its simplicity, this Chern-Simons action should form a fruitful starting point for analysing perturbative properties of Yang-Mills theory.

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arXiv2024

Three-dimensional $\operatorname{SL}(2,\mathbb R)$ Yang-Mills theory is three-dimensional gravity with background sources

Chern-Simons theory with certain gauge groups is known to be equivalent to a first-order formulation of three-dimensional Einstein gravity with a cosmological constant, where both are purely topological. Here, we extend this correspondence to theories with dynamical degrees of freedom. We show that three-dimensional Yang-Mills theory with gauge group $\operatorname{SL}(2,\mathbb R)$ is equivalent to the first-order formulation of three-dimensional Einstein gravity with no cosmological constant coupled to a background stress-energy tensor density (which breaks the diffeomorphism symmetry). The local degree of freedom of three-dimensional Yang-Mills theory corresponds to degenerate "gravitational waves" in which the metric is degenerate and the spin connection is no longer completely determined by the metric. Turning on a cosmological constant produces the third-way (for $\Lambda<0$) or the imaginary third-way (for $\Lambda>0$) gauge theories with a background stress-energy tensor density.

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arXiv2024

Out-of-time-order asymptotic observables are quasi-isomorphic to time-ordered amplitudes

Asymptotic observables in quantum field theory beyond the familiar $S$-matrix have recently attracted much interest, for instance in the context of gravity waveforms. Such observables can be understood in terms of Schwinger-Keldysh-type 'amplitudes' computed by a set of modified Feynman rules involving cut internal legs and external legs labelled by time-folds. In parallel, a homotopy-algebraic understanding of perturbative quantum field theory has emerged in recent years. In particular, passing through homotopy transfer, the $S$-matrix of a perturbative quantum field theory can be understood as the minimal model of an associated (quantum) $L_\infty$-algebra. Here we bring these two developments together. In particular, we show that Schwinger-Keldysh amplitudes are naturally encoded in an $L_\infty$-algebra, similar to ordinary scattering amplitudes. As before, they are computed via homotopy transfer, but using deformation-retract data that are not canonical (in contrast to the conventional $S$-matrix). We further show that the $L_\infty$-algebras encoding Schwinger-Keldysh amplitudes and ordinary amplitudes are quasi-isomorphic (meaning, in a suitable sense, equivalent). This entails a set of recursion relations that enable one to compute Schwinger-Keldysh amplitudes in terms of ordinary amplitudes or vice versa.

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