arXiv subjects

Hyungrok Kim

Publications and source records attributed to Hyungrok Kim.

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

Non-relativistic limits of $\mathcal N=4$ supersymmetric Yang-Mills theory and S-duality

We investigate non-relativistic limits of four-dimensional maximally supersymmetric Yang-Mills theory (4d MSYM) and their relation to the nonperturbative $\operatorname{SL}(2;\mathbb Z)$ S-duality of the relativistic theory. We construct a general family of non-relativistic limits using a Type IIB brane set-up with a D3-brane and $(p,q)$-strings and show that the resulting theories are topological deformations of supersymmetric Galilean Yang-Mills theory or quantum mechanics on the moduli space of BPS monopoles. The deformations of the Galilean Yang-Mills theory are the familiar $\theta$-term and a coupling to the monopole charge, while in the moduli space theory the only deformation is a $\theta$-term. This family of theories fit together into a three-dimensional moduli space with nontrivial topology, on which $\operatorname{PSL}(2;\mathbb Z)$-valued dualities act in a richer and more complex way than in the relativistic parent theory. In the Abelian case, we establish the duality directly using the path integral, while in the non-Abelian case we support our claim by matching the one-particle spectrum as well as the Galilean spacetime symmetries and electric/magnetic invertible one-form symmetries.

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arXiv2026

Generalised Symmetries and Swampland-Type Constraints from Charge Quantisation via Rational Homotopy Theory

Sati and Schreiber [arXiv:2402.18473, arXiv:2512.12431] have proposed that charge quantisation in quantum field theory and string theory is governed by a homotopy type $\mathcal A$. We provide a refinement of this postulate, incorporating other currents including matter, connecting it to adjustments in higher gauge theory and providing a prescription for determining $\mathcal A$, and show that, while the homotopy groups of $\mathcal A$ classify the possible brane charges, the homology groups of $\mathcal A$ classify the invertible higher-form symmetries. Furthermore, we show that the charge-quantisation postulate implies a number of non-trivial constraints on quantum field theories similar to those implied by swampland conjectures; in particular, it rules out noncompact gauge groups and one-form field strengths that form a non-nilpotent Lie algebra. Finally, we argue that for theories of quantum gravity the space $\mathcal A$ must be contractible, in accordance with the swampland conjectures on the absence of global generalised symmetries and the completeness of the spectrum of charges, and explain how this explicitly arises in the case of Type I string theory.

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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

Which Functions Admit a Positive Geometry? From Branch Cuts to String Amplitudes

Positive geometry provides a geometric framework where physical observables are encoded as canonical forms associated to regions of kinematic space. In this paper we consider a generalisation to an infinite union of line segments, which allows us to capture canonical forms beyond rational functions. In the continuum limit of positive geometries, we show that we can generalise even further and describe positive geometries whose canonical forms contain branch cuts. We will constrain which functions can be obtained as the canonical form of one-dimensional positive geometries. We introduce the notion of the pseudogenus to classify meromorphic functions, and show that canonical forms can be written as the $\mathrm d\log$ of a function with pseudogenus zero. Furthermore, we argue that the spectrum encoded by a union of line segments is consistent with the presence of a stringy tower of states or a Kaluza-Klein tower with three or more compact directions only if nearly all such states do not contribute to the scattering amplitude. In addition, we show how the d log of both open and closed string amplitudes admits a positive geometry. This allows us to give a fully geometric interpretation for the KLT double copy at four points.

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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

Hydrodynamics as cospans of field theories into the BF theory

Hydrodynamics is based on conservation laws of currents: one starts from the conserved currents of the theory describing the microscopic dynamics, and provides an alternative parameterisation of these currents in terms of hydrodynamic variables (density, pressure, velocity, etc.). This paradigm has recently been extended to incorporate higher-form symmetries. The conservation law of the $p$-form conserved currents can be regarded as the equations of motion of a $BF$ theory that treats the currents as fundamental fields. We argue that the hydrodynamic approximation to a microscopic theory can be regarded as a cospan of differential graded manifolds $X_\mathrm{micro}\to X_{BF}\leftarrow X_\mathrm{hydro}$, where $X_\mathrm{micro}$ and $X_\mathrm{hydro}$ describe the microscopic and hydrodynamic theories, respectively, and $X_{BF}$ describes the $BF$ theory of conserved currents.

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arXiv2026

Emergent fracton strings from covariant bi-form gauge field theory

We present a covariant field-theoretical framework for a rank-4 tensor gauge field theory describing fractonic string-like objects. We show that the most general quadratic, parity-preserving action naturally leads to a Maxwell-like sector, with tensorial analogues of electric and magnetic fields, Maxwell-like equations, a conserved energy-momentum tensor, and a Lorentz-like force. Remarkably, the theory gives rise to fracton-like string excitations purely from symmetry principles: constraints on the motion of these extended objects appear as Gauss-like laws, without being imposed by hand. One of these laws is new and corresponds to a generalised dipole conservation for closed strings, restricting their mobility and defining a novel class of fractonic string-like excitations. Finally, we uncover a connection to linearised area-metric gravity: in a suitable limit, the theory reduces to known covariant fracton models with rank-2 gauge fields, highlighting a deep link between fractonic matter and gravity-like structures. This provides a unified perspective on higher-rank gauge fields, extended excitations, and emergent gravitational features.

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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

$L_\infty$-algebraic extensions of non-Lorentzian kinematical Lie algebras, gravities, and brane couplings

The Newtonian limit of Newton-Cartan gravity relies crucially on the Lie-algebraic central extension to the Galilean algebra, namely the Bargmann algebra. Lie-algebraic central extensions naturally generalise to $L_\infty$-algebraic central extensions, which in turn classify branes in superstring theory via the brane bouquet. This paper classifies all $L_\infty$-algebraic central extensions of all kinematical Lie algebras that do not depend on the spatial rotation generators as well as all iterated central extensions thereof (for codimensions $\le3$). The Bargmann central extension of the Galilean algebra then appears as merely one term in a sequence of $L_\infty$-algebraic central extensions in each degree; a similar situation obtains for the Newton-Hooke algebra and the static algebra, but not for the Carrollian algebra nor those kinematical Lie algebras that are not Wigner-\.In\"on\"u deformations of a simple algebra. The sequence of $L_\infty$-algebraic central extensions in each degree then corresponds to a tower of $p$-form fields. After imposing conventional constraints, the zero-form field provides absolute time, and the higher-form fields are certain wedge products of the field strengths of the one-form (Bargmann) gravitational field. These then provide natural $(p-1)$-brane couplings to the corresponding non-Lorentzian gravities, which are found to produce velocity-dependent gravitational effects in the presence of torsion. The $L_\infty$-algebraic cocycles also provide Wess-Zumino-Witten terms for the $(p-1)$-brane action, which require the introduction of doubled spatial coordinates that are reminiscent of double field theory, but which (in some cases at least, and given appropriate kinetic terms) do not result in doubled physics.

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arXiv2025

Generalised wavefunction coefficients and acyclonesto-cosmohedra

Scattering amplitudes of $\operatorname{tr}(ϕ^3)$ theory can be encoded as the canonical form of the Stasheff associahedron. Similarly, the flat-space wavefunction coefficients of the same theory are captured by the recently proposed cosmohedron, a non-simple polytope associated to the Stasheff associahedron; unitarity and locality of the amplitudes and wavefunction coefficients are then encoded in the factorisation properties of faces of these polytopes. In this paper, we argue that these desirable properties of the Stasheff associahedron are shared by a wider class of polytopes called acyclonestohedra and generalise the cosmohedron construction to arbitrary acyclonestohedra. Acyclonestohedra are generalisations of Stasheff associahedra and graph associahedra defined on the data of a partially ordered set or, more generally, an acyclic realisable matroid on a building set. When the acyclonestohedron is associated to a partially ordered set, it may be interpreted as arising from Chan-Paton-like factors that are only (cyclically) partially ordered, rather than (cyclically) totally ordered as for the ordinary open string. In this paper, we argue that the canonical forms of acyclonestohedra encode scattering-amplitude-like objects that factorise onto themselves, thereby extending recent results for graph associahedra, and construct truncations of acyclonestohedra into acyclonesto-cosmohedra whose canonical forms may be interpreted as encoding a generalisation of the cosmological wavefunction coefficients. As a byproduct, we provide evidence that acyclonesto-cosmohedra can be obtained as sections of graph cosmohedra.

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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

$E_2L_\infty$-algebras, Generalized Geometry, and Tensor Hierarchies

We define a generalized form of $L_\infty$-algebras called $E_2L_\infty$-algebras. As we show, these provide the natural algebraic framework for generalized geometry and the symmetries of double field theory as well as the gauge algebras arising in the tensor hierarchies of gauged supergravity. Our perspective shows that the kinematical data of the tensor hierarchy is an adjusted higher gauge theory, which is important for developing finite gauge transformations as well as non-local descriptions. Mathematically, $E_2L_\infty$-algebras shed some light on Loday's problem of integrating Leibniz algebras.

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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

Strings as Hyper-Fractons

We systematically examine all possible Gauss laws obeying spatial rotation symmetry, characterising the corresponding conserved charges. In the case of conserved higher moments, this gives rise to fractonic behaviour. We show that many Gauss laws, including those arising from $p$-form electrodynamics, in fact, produce an infinite tower of conserved moments, which we dub hyper-fractonic. In hyper-fractonic systems, a finite number of charged particles cannot be mobile due to an inability of fulfilling the infinite number of conservation laws with a finite number of degrees of freedom. Instead, mobile charged objects must have an infinite number of degrees of freedom. In particular, the strings and branes naturally coupling to $p$-form potentials provide an example of hyper-fractonic matter.

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