arXiv subjects

Euihun Joung

Publications and source records attributed to Euihun Joung.

At least 19 recordsLinked to original sources

arXiv2026

Worldline Higher Spin Gravity

We propose a worldline formulation of higher-spin gravity (HSG) in $\mathrm{AdS}_4$, based on a simple twistor action. Taken at face value, the model describes only the free propagation of massless higher-spin fields. The central observation of this work is that the model admits a natural double-line interpretation, which supplies a geometric prescription for gluing worldlines at interaction vertices, in close parallel with the joining of strings in string theory. Building on this picture, we construct $\mathrm{AdS}$-covariant vertex operators for all massless higher-spin fields, show that they satisfy the Bargmann-Wigner equations, and use them to compute the n-point correlation functions of type-A and type-B HSG as worldline path integrals of these vertex operators. In the boundary limit these correlators reproduce the higher-spin current correlators of free boson and free fermion vector models. We further discuss the embedding of the worldline theory into Poisson sigma model, where the doubled-line structure acquires a geometric origin as the two edges of an open string worldsheet, together with several consequences of this enlarged framework -- fractional branes, loop expansion, unoriented projection, and the prospect of a worldsheet formulation of HSG.

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arXiv2026

Manifest duality and Lorentz covariance for linearised gravity as edge modes

We present the first formulation of linearised gravity in four dimensions which is manifestly Lorentz covariant and democratic, i.e. treats the two frames related by electric-magnetic duality on equal footing. It is well-known that four-dimensional linearised gravity belongs to a class of singleton representations of the four-dimensional conformal algebra $\mathfrak{so}(2,4)$. Our key insight is viewing this algebra as the isometry of $\text{AdS}_5$ and realising the massless spin-2 field as an edge mode of a five-dimensional topological field taking values in a specific finite-dimensional representation of $\mathfrak{so}(2,4)$. The desired four-dimensional action is then found by a covariant boundary reduction procedure.

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arXiv2025

Extracting Edge Modes: Reduction of 3D and 2D Gravities

We investigate the boundary reduction of 3D Einstein gravity and JT gravity into their respective edge mode theories - namely, the Liouville and Alekseev-Shatashvili, and Schwarzian models. By examining the roles of boundary conditions, canonical transformations, and differing formulations - metric versus Chern-Simons - we clarify how physical degrees of freedom become localized at the boundary and resolve several long-standing ambiguities in the reduction procedure.

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arXiv2025

Higher-order chiral scalar from boundary reduction of 3d higher-spin gravity

We use a recently proposed covariant procedure to reduce the Chern-Simons action of three-dimensional higher-spin gravity to the boundary, resulting in a Lorentz covariant action for higher-order chiral scalars. After gauge-fixing, we obtain a higher-derivative action generalizing the $s=1$ Floreanini-Jackiw and $s=2$ Alekseev-Shatashvili actions to arbitrary spin $s$. For simplicity, we treat the case of general spin at the linearized level, while the full non-linear asymptotic boundary conditions are presented in component form for the $SL(3,\mathbb R)$ case. Finally, we extend the spin-3 linearized analysis to a background with non-trivial higher-spin charge and show that it has a richer structure of zero modes.

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arXiv2024

Manifestly Covariant Worldline Actions from Coadjoint Orbits. Part I: Generalities and Vectorial Descriptions

We derive manifestly covariant actions of spinning particles starting from coadjoint orbits of isometry groups, by using Hamiltonian reductions. We show that the defining conditions of a classical Lie group can be treated as Hamiltonian constraints which generate the coadjoint orbits of another, dual, Lie group. In case of (inhomogeneous) orthogonal groups, the dual groups are (centrally-extended inhomogeneous) symplectic groups. This defines a symplectic dual pair correspondence between the coadjoint orbits of the isometry group and those of the dual Lie group, whose quantum version is the reductive dual pair correspondence à la Howe. We show explicitly how various particle species arise from the classification of coadjoint orbits of Poincaré and (A)dS symmetry. In the Poincaré case, we recover the data of the Wigner classification, which includes continuous spin particles, (spinning) tachyons and null particles with vanishing momenta, besides the usual massive and massless spinning particles. In (A)dS case, our classification results are not only consistent with the pattern of the corresponding unitary irreducible representations observed in the literature, but also contain novel information. In dS, we find the presence of partially massless spinning particles, but continuous spin particles, spinning tachyons and null particles are absent. The AdS case shows the largest diversity of particle species. It has all particles species of Poincaré symmetry except for the null particle, but allows in addition various exotic entities such as one parameter extension of continuous particles and conformal particles living on the boundary of AdS. Notably, we also find a large class of particles living in "bitemporal" AdS space, including ones where mass and spin play an interchanged role. We also discuss the relative inclusion structure of the corresponding orbits.

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arXiv2024

Manifestly Covariant Worldline Actions from Coadjoint Orbits. Part II: Twistorial Descriptions

Worldline actions for various twistor particles in AdS spacetimes are constructed from the coadjoint orbits of $Sp(4,\mathbb R)$, $SU(2,2)$ and $O^*(8)$ as constrained Hamiltonian systems. The constraints are associated with the coadjoint orbits of the dual groups, respectively identified as $O(p,M-p)$, $U(p, M-p)$ and $Sp(p, M-p)$. These actions are presented in a universal form by making use of the twistor variables taking value in $\mathbb R$, $\mathbb C$ and $\mathbb H$, respectively. We find that the massless, massive and the conformal particles (namely the singletons) of any spins appear for the compact dual groups with $p=0$ reproducing many of the results in earlier literature, whereas more exotic particle species, such as various tachyons, continuous spin particles and BdS particles appear for the non-compact dual groups.

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arXiv2024

Gravitational Edge Mode in Asymptotically AdS$_2$: JT Gravity Revisited

We study the gravitational edge mode of the Jackiw-Teitelboim (JT) gravity and its $sl(2,\mathbb{R})$ BF theory description with the asymptotic AdS$_2$ boundary condition. We revisit the derivation of the Schwarzian theory from the wiggling boundary as an action for the gravitational edge mode. We present an alternative description for the gravitational edge mode from the metric fluctuation with the fixed boundary, which is often referred as "would-be gauge mode". We clarify the relation between the wiggling boundary and the would-be gauge mode. We demonstrate a natural top-down derivation of $PSL(2,\mathbb{R})$ gauging and the path integral measure of the Schwarzian theory. In the $sl(2,\mathbb{R})$ BF theory, we incorporate the gravitational edge mode and derive the Schwarzian theory with $PSL(2,\mathbb{R})$ gauging. We also discuss the path integral measure from the Haar measure in the Iwasawa decomposition of $PSL(2,\mathbb{R})$.

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arXiv2024

Spinor-helicity representations of (A)dS$_4$ particles of any mass

The spinor-helicity representations of massive and (partially-)massless particles in four dimensional (Anti-) de Sitter spacetime are studied within the framework of the dual pair correspondence. We show that the dual groups (aka "little groups") of the AdS and dS groups are respectively $O(2N)$ and $O^*(2N)$. For $N=1$, the generator of the dual algebra $\mathfrak{so}(2)\cong \mathfrak{so}^*(2) \cong \mathfrak{u}(1)$ corresponds to the helicity operator, and the spinor-helicity representation describes massless particles in (A)dS$_4$. For $N=2$, the dual algebra is composed of two ideals, $\mathfrak{s}$ and $\mathfrak{m}_Λ$. The former ideal $\mathfrak{s}\cong \mathfrak{so}(3)$ fixes the spin of the particle, while the mass is determined by the latter ideal $\mathfrak{m}_Λ$, which is isomorphic to $\mathfrak{so}(2,1)$, $\mathfrak{iso}(2)$ or $\mathfrak{so}(3)$ depending on the cosmological constant being positive, zero or negative. In the case of a positive cosmological constant, namely dS$_4$, the spinor-helicity representation contains all massive particles corresponding to the principal series representations and the partially-massless particles corresponding to the discrete series representations leaving out only the light massive particles corresponding to the complementary series representations. The zero and negative cosmological constant cases, which had been addressed in earlier references, are also discussed briefly. Finally, we consider the multilinear form of helicity spinors invariant under (A)dS group, which can be served for the (A)dS counterpart of the scattering amplitude, and discuss technical differences and difficulties of the (A)dS cases compared to the flat spacetime case.

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arXiv2023

Democracy from topology

Chiral form fields in $d$ dimensions can be effectively described as edge modes of topological Chern-Simons theories in $d+1$ dimensions. At the same time, manifestly Lorentz-invariant Lagrangian description of such fields directly in terms of a $d$-dimensional field theory is challenging and requires introducing nontrivial auxiliary gauge fields eliminated on-shell with extra gauge symmetries. A recent work by Arvanitakis et al.\ demonstrates (emphasizing the case of 2d chiral bosons) that the two approaches are related, and a peculiar reduction on the $(d+1)$-dimensional topological Lagrangian automatically leads to $d$-dimensional Lagrangians with appropriate sets of auxiliary fields. We develop this setup in three distinct directions. First, we demonstrate how arbitrary Abelian self-interactions for chiral forms can be included using nonlinear boundary terms in the Chern-Simons theory. Second, by generalizing the Chern-Simons theory to the BF theory, we obtain an analogous democratic description of non-chiral form fields, where electric and magnetic potentials appear as explicit dynamical variables. Third, we discuss the effects of introducing topological interactions in the higher-dimensional bulk, which produce extra interaction terms in the boundary theory. When applied to a topological 4-form field in 12 dimensions, this construction results in a democratic description of the 3-form gauge field of the 11-dimensional supergravity.

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arXiv2022

Color decorations of Jackiw-Teitelboim gravity

We introduce the colored version of Jackiw-Teitelboim (JT) gravity which is the two-dimensional dilaton gravity model with matrix-valued fields. It is straightforwardly formulated in terms of BF action with $su(N,N)$ gauge algebra so that the standard JT gravity is embedded as $su(1,1) \subset su(N,N)$ subsector. We also elaborate on the respective metric formulation which is shown to involve the JT fields plus $su(N)$ non-Abelian fields as well as $su(N)$-matrix valued metric and dilaton fields. Their interactions are governed by minimal couplings and potential terms of cubic and quartic orders involving derivatives.

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arXiv2022

Schwarzian for colored Jackiw-Teitelboim gravity

We study the boundary effective action of the colored version of the Jackiw-Teitelboim (JT) gravity. We derive the boundary action, which is the color generalization of the Schwarzian action, from the $su(N,N)$ BF formulation of the colored JT gravity. Using different types of the $SU(N,N)$ group decompositions both the zero and finite temperature cases are elaborated. We provide the semi-classical perturbative analysis of the boundary action and discuss the instability of the spin-1 mode and its implication for the quantum chaos. A rainbow-AdS$_2$ geometry is introduced where the color gauge symmetry is spontaneously broken.

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arXiv2021

Colourful Poincaré symmetry, gravity and particle actions

We construct a generalisation of the three-dimensional Poincaré algebra that also includes a colour symmetry factor. This algebra can be used to define coloured Poincaré gravity in three space-time dimensions as well as to study generalisations of massive and massless free particle models. We present various such generalised particle models that differ in which orbits of the coloured Poincaré symmetry are described. Our approach can be seen as a stepping stone towards the description of particles interacting with a non-abelian background field or as a starting point for a worldline formulation of an associated quantum field theory.

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arXiv2021

Unfolding Conformal Geometry

Conformal geometry is studied using the unfolded formulation à la Vasiliev. Analyzing the first-order consistency of the unfolded equations, we identify the content of zero-forms as the spin-two off-shell Fradkin-Tseytlin module of $\mathfrak{so}(2,d)$. We sketch the nonlinear structure of the equations and explain how Weyl invariant densities, which Type-B Weyl anomaly consist of, could be systematically computed within the unfolded formulation. The unfolded equation for conformal geometry is also shown to be reduced to various on-shell gravitational systems by requiring additional algebraic constraints.

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arXiv2020

Dual Pair Correspondence in Physics: Oscillator Realizations and Representations

We study general aspects of the reductive dual pair correspondence, also known as Howe duality. We make an explicit and systematic treatment, where we first derive the oscillator realizations of all irreducible dual pairs: $(GL(M,\mathbb R), GL(N,\mathbb R))$, $(GL(M,\mathbb C), GL(N,\mathbb C))$, $(U^*(2M), U^*(2N))$, $(U(M_+,M_-), U(N_+,N_-))$, $(O(N_+,N_-),Sp(2M,\mathbb R))$, $(O(N,\mathbb C), Sp(2M,\mathbb C))$ and $(O^*(2N), Sp(M_+,M_-))$. Then, we decompose the Fock space into irreducible representations of each group in the dual pairs for the cases where one member of the pair is compact as well as the first non-trivial cases of where it is non-compact. We discuss the relevance of these representations in several physical applications throughout this analysis. In particular, we discuss peculiarities of their branching properties. Finally, closed-form expressions relating all Casimir operators of two groups in a pair are established.

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arXiv2020

A note on Faddeev--Popov action for doubled-yet-gauged particle and graded Poisson geometry

The section condition of Double Field Theory has been argued to mean that doubled coordinates are gauged: a gauge orbit represents a single physical point. In this note, we consider a doubled and at the same time gauged particle action, and show that its BRST formulation including Faddeev--Popov ghosts matches with the graded Poisson geometry that has been recently used to describe the symmetries of Double Field Theory. Besides, by requiring target spacetime diffeomorphisms at the quantum level, we derive quantum corrections to the classical action involving dilaton, which might be comparable with the Fradkin--Tseytlin term on string worldsheet.

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arXiv2019

A note on higher-order vertices of higher-spin fields in flat and (A)dS space

In this work we classify homogeneous solutions to the Noether procedure in (A)dS for an arbitrary number of external legs and in general dimensions. We also give a review of the corresponding flat space classification and its relation with the (A)dS result presented here. The role of dimensional dependent identities is also investigated.

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arXiv2019

Looking for partially-massless gravity

We study the possibility for a unitary theory of partially-massless (PM) spin-two field interacting with Gravity in arbitrary dimensions. We show that the gauge and parity invariant interaction of PM spin two particles requires the inclusion of specific massive spin-two fields and leads to a reconstruction of Conformal Gravity, or multiple copies of the latter in even dimensions. By relaxing the parity invariance, we find a possibility of a unitary theory in four dimensions, but this theory cannot be constructed in the standard formulation, due to the absence of the parity-odd cubic vertex therein. Finally, by relaxing the general covariance, we show that a `non-geometric' coupling between massless and PM spin-two fields may lead to an alternative possibility of a unitary theory. We also clarify some aspects of interactions between massless, partially-massless and massive fields, and resolve disagreements in the literature.

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arXiv2018

Conformal Higher-Spin Gravity: Linearized Spectrum = Symmetry Algebra

The linearized spectrum and the algebra of global symmetries of conformal higher-spin gravity decompose into infinitely many representations of the conformal algebra. Their characters involve divergent sums over spins. We propose a suitable regularization adapted to their evaluation and observe that their characters are actually equal. This result holds in the case of type-A and type-B (and their higher-depth generalizations) theories and confirms previous observations on a remarkable rearrangement of dynamical degrees of freedom in conformal higher-spin gravity after regularization.

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