David Osten

A bstract: In this paper we construct duality-covariant worldvolume dynamics of particles and branes. We extend known actions and phase space formulations to include the hidden E ₈ symmetry of 11D supergravity, analogous to the Ehlers symmetry of 4D gravity. Making the worldvolume theory manifestly duality-covariant requires the ancillary structure of E ₈ exceptional field theory to be taken into account. For zero-branes, we propose an enlarged worldline model with a coadjoint orbit term to encode this. More generally, we propose worldvolume theories for arbitrary exotic branes in a way that generalises the known gauged sigma model of the Kaluza-Klein monopole. These are natural in the duality-covariant Hamiltonian formulation employed here. We discuss the case of zero-branes in eleven dimensions as an illustrative example.

Cartan geometry provides a unifying algebraic construction of curvature and torsion, based on an underlying model Lie algebra; a viewpoint that can be extended naturally to the higher algebraic structures underlying supergravity. We present a Cartan-geometric framework for generalized geometries governed by a differential graded Lie algebra, extending previous results. The extended tangent bundle admits the action of both a global duality group G and a local gauge group H . This algebraic structure is implemented via a brane current algebra; the phase space Poisson structure of p -branes. Within this Cartan-inspired framework, we define a hierarchy of generalized connections and compute their linearized torsion and curvature tensors, including the higher curvatures required by the tensor hierarchy. This provides a systematic construction of curvature and torsion tensors in generic generalized geometries.

This paper proposes a novel decoupling limit of the membrane, leading to the ( 1 + 2 )-dimensional classically integrable model originally introduced by Manakov, Zakharov, and Ward. This limit is the large-wrapping regime of a membrane propagating toy background of the form R t × T 2 × G subject to scaling limit, where G is a Lie group and the geometry is supported by a four-form flux. Such toy backgrounds can arise from consistent eleven-dimensional supergravity solutions, exemplified by the uplift of the pure Neveu-Schwarz-Neveu-Schwarz AdS 3 × S 3 × T 4 background. The scaling limit can be interpreted as a simultaneous small tension and non- or hyperrelativistic limit.

Duality covariant curvature and torsion tensors in double field theory/generalized geometry are central in analyzing consistent truncations, generalized dualities, and related integrable σ-models. They are constructed systematically with the help of a larger, auxiliary space in a procedure inspired by Cartan geometry originally proposed by Poláček and Siegel for bosonic strings. It pivots around a maximally isotropic group that captures the generalized structure group of the physical space. We show how dropping the isotropy condition on this group allows us to describe heterotic/type I strings. As an immediate application, we construct a new family of heterotic backgrounds that interpolates between the two-dimensional cigar and trumpet backgrounds.

Dimensional reduction of gravity theories to D = 2 along commuting Killing isometries is well-known to be classically integrable. The resulting system typically features a coset σ-model coupled to a dilaton and a scale factor of the dimensional reduction. In this article, we construct two families of deformations of dimensionally reduced gravity that preserve the Lax integrable structure. The first family is an extension of the Auxiliary Field Deformation recently introduced by Ferko and Smith, while the second family consists in the embedding of the Yang-Baxter σ-model into D = 2 dimensionally reduced gravity. For both deformations we construct flat Lax representations. The Auxiliary Field Deformation, in particular, preserves the rich algebraic structure underlying the undeformed model and, leaving the canonical structure of the Lax connection’s spatial components essentially unchanged, allows us to prove its integrability also in the Hamiltonian sense.

Duality covariant curvature and torsion tensors in double field theory/generalized geometry are central in analyzing consistent truncations, generalized dualities, and related integrable $σ$-models. They are constructed systematically with the help of a larger, auxiliary space in a procedure inspired by Cartan geometry originally proposed by Poláček and Siegel for bosonic strings. It pivots around a maximally isotropic group that captures the generalized structure group of the physical space. We show how dropping the isotropy condition on this group allows us to describe heterotic/type I strings. As an immediate application, we construct a new family of heterotic backgrounds that interpolates between the two-dimensional cigar and trumpet backgrounds.

This article shows that the approach to generalized curvature and torsion pioneered by Poláček and Siegel [Natural curvature for manifest T-duality, .] is a generalization of Cartan geometry—rendering latter natural from the point of view of O ( d , d ) -generalized geometry. We present this approach in the generalized metric formalism and show that almost all parts of the additional higher generalized tensors appearing in this approach correspond to covariant derivatives of the generalized Riemann tensor. As an application, we use this framework to phrase σ -model dynamics in an explicitly covariant way—both under generalized diffeomorphisms and local gauge transformations. Published by the American Physical Society 2024

We prove the existence of a family of integrable deformations of ℤ _N -coset models in two dimensions. Our approach uses and generalises the method of auxiliary fields that was recently introduced for the principal chiral model by Ferko and Smith.

The known stringy non-relativistic (NR) limit of the universal NS-NS sector of supergravity has a finite Lagrangian due to non-trivial cancellations of divergent parts coming from the metric and the B-field. We demonstrate that in Double Field Theory (DFT) and generalised geometry these cancellations already happen at the level of the generalised metric, which is convergent in the limit c → ∞, implying that the NR limit can be imposed before solving the strong constraint. We present the c-expansion of the generalised metric, which reproduces the Non-Riemannian formulation of DFT at the (finite) leading order, and the c-expansion of the generalised frame, which contains divergences. We also extend this approach to the non-Abelian gauge field of Heterotic DFT assuming a convergent expansion for the O(D, D + n) generalised metric. From this proposal, we derive a novel c-expansion for the bosonic part of the heterotic supergravity which is, by construction, compatible with O(D, D)-symmetry.