arXiv subjects

Richard Van Dongen

Publications and source records attributed to Richard Van Dongen.

9 recordsLinked to original sources

arXiv2026

Dirichlet, Neumann, Mixed and self-dual holography: (self-dual) Yang-Mills theory

Motivated by applications of self-dual theories to the AdS/CFT correspondence, we study self-dual Yang-Mills theory (SDYM) and its relation to Yang-Mills theory and to Chalmers-Siegel theory with Dirichlet, Neumann, and mixed boundary conditions. A Fefferman-Graham analysis of SDYM is performed to identify its boundary CFT data. We make a proposal for self-dual holography that defines $3d$ ``self-dual CFTs''. The bulk-to-bulk and boundary-to-bulk propagators for SDYM and for Yang-Mills/Chalmers-Siegel theory with mixed boundary conditions are derived in Feynman and axial gauges. Three- and four-point functions are computed in the spinor-helicity formalism, and the relations among the results in the various theories are clarified. The flat limit and the gauge-(in)dependence of the results are analyzed.

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arXiv2026

Dirichlet, Neumann, Mixed and self-dual holography: (self-dual) Yang--Mills theory II

We consider Yang--Mills, Chalmers--Siegel and self-dual Yang--Mills (SDYM) theories within AdS/CFT correspondence. Bulk-to-bulk and boundary-to-bulk propagators are derived in various gauges and for Dirichlet, Neumann, mixed and self-dual boundary conditions. Three- and four-point holographic correlators are computed in the three theories to establish the relation between the observables thereof. This is a companion paper to [arXiv:2602.21658].

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arXiv2026

Self-dual holography: four-point AdS/CFT correlators in higher-spin gravity

Self-dual theories, being UV-finite, should have their own AdS/CFT dualities. Higher-spin extensions of self-dual theories are attractive to simplify the CFT duals. The maximal self-dual theory is Chiral higher-spin gravity, which should be dual to a subsector of Chern--Simons matter theories. As a step toward establishing self-dual holography, we develop the Fefferman--Graham expansion and holographic dictionary for arbitrary spin self-dual theories. As an application, we derive bulk-to-bulk propagators and compute three- and four-point AdS/CFT correlators in a contraction of Chiral higher-spin gravity, which is a higher-spin extension of self-dual Yang--Mills theory.

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arXiv2024

Strong Homotopy Algebras for Chiral Higher Spin Gravity via Stokes Theorem

Chiral higher spin gravity is defined in terms of a strong homotopy algebra of pre-Calabi-Yau type (noncommutative Poisson structure). All structure maps are given by the integrals over the configuration space of concave polygons and the first two maps are related to the (Shoikhet-Tsygan-)Kontsevich Formality. As with the known formality theorems, we prove the $A_\infty$-relations via Stokes' theorem by constructing a closed form and a configuration space whose boundary components lead to the $A_\infty$-relations. This gives a new way to formulate higher spin gravities and hints at a construct encompassing the known formality theorems.

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arXiv2023

Minimal model of Chiral Higher Spin Gravity

A unique class of local Higher Spin Gravities with propagating massless fields in $4d$ - Chiral Higher Spin Gravity - was first found in the light-cone gauge. We construct a covariant form of the corresponding field equations in all orders, thus completing the previous analysis of arXiv:2204.10285. This result is equivalent to taking the minimal model (in the sense of $L_\infty$-algebras) of the jet-space BV-BRST formulation of Chiral Higher Spin Gravity, thereby, containing also information about counterterms, anomalies, etc.

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arXiv2023

Chiral Higher Spin Gravity and Convex Geometry

Chiral Higher Spin Gravity is the minimal extension of the graviton with propagating massless higher spin fields. It admits any value of the cosmological constant, including zero. Its existence implies that Chern-Simons vector models have closed subsectors and supports the $3d$ bosonization duality. In this letter, we explicitly construct an $A_\infty$-algebra that determines all interaction vertices of the theory. The algebra turns out to be of pre-Calabi-Yau type. The corresponding products, some of which originate from Shoikhet-Tsygan-Kontsevich formality, are given by integrals over the configuration space of convex polygons.

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arXiv2022

More on Chiral Higher Spin Gravity and Convex Geometry

Recently, a unique class of local Higher Spin Gravities with propagating massless fields in $4d$ - Chiral Higher Spin Gravity - was given a covariant formulation both in flat and $(A)dS_4$ spacetimes at the level of equations of motion. We unfold the corresponding homological perturbation theory as to explicitly obtain all interaction vertices. The vertices reveal a remarkable simplicity after an appropriate change of variables. Similarly to formality theorems the $A_\infty/L_\infty$ multi-linear products can be represented as integrals over a configuration space, which in our case is the space of convex polygons. The $A_\infty$-algebra underlying Chiral Theory is of pre-Calabi-Yau type. As a consequence, the equations of motion have the Poisson sigma-model form.

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arXiv2022

Minimal models of field theories: Chiral Higher Spin Gravity

There exists a unique class of local Higher Spin Gravities with propagating massless fields in $4d$ - Chiral Higher Spin Gravity. Originally, it was formulated in the light-cone gauge. We construct a covariant form of this theory as a Free Differential Algebra up to NLO, i.e. at the level of equations of motion. It also contains the recently discovered covariant forms of the higher spin extensions of SDYM and SDGR, as well as SDYM and SDGR themselves. From the mathematical viewpoint the result is equivalent to taking the minimal model (in the sense of $L_\infty$-algebras) of the jet-space extension of the BV-BRST formulation of Chiral Higher Spin Gravity, thereby, containing also information about (presymplectic AKSZ) action, counterterms, anomalies, etc.

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arXiv2022

Minimal models of field theories: SDYM and SDGR

There exists a natural $L_\infty$-algebra or $Q$-manifold that can be associated to any (gauge) field theory. Perturbatively, it can be obtained by reducing the $L_\infty$-algebra behind the jet space BV-BRST formulation to its minimal model. We explicitly construct the minimal models of self-dual Yang-Mills and self-dual gravity theories, which also represents their equations of motion as Free Differential Algebras. The minimal model regains all relevant information about the field theory, e.g. actions, charges, anomalies, can be understood in terms of the corresponding $Q$-cohomology.

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