ABSTRACT We propose a description of T‐duality between general geometric and non‐geometric backgrounds as higher groupoid bundles with connections. Our description extends the previous observation by Nikolaus and Waldorf that the topological aspects of geometric and half‐geometric T‐dualities can be described in terms of higher geometry. We extend their construction in two ways. First, we endow the higher geometries with adjusted connections, which allow us to discuss explicit formulas for the metric and the Kalb–Ramond field of a T‐background. Second, we extend the principal 2‐bundles to principal 2‐groupoid bundles, which accommodate the scalar fields arising in T‐dualities along two directions as well as ‐fluxes. Our proposals reproduce key examples from the literature. They are manifestly covariant under the full T‐duality group and have interesting physical and mathematical implications. Eventually, we also comment on the case of T‐duality in the presence of scalar fluxes.
ABSTRACT We derive the generic higher multipole perturbation theory of asymptotically flat branch I black holes in quartic SU(2) Proca theory. The static geometry depends only on , but nonspherical perturbations resolve the independent ratio . A constraint analysis before harmonic reduction identifies eleven physical modes and shows that the reduced physical principal system at finite radius is locally strongly hyperbolic precisely for . Diagonal rotation harmonics divide these modes into six axial and five polar amplitudes. We derive both coupled radial systems including their Proca and Einstein constraints. One polar channel decouples exactly, with exterior potential ; an energy identity therefore excludes every exponentially growing quasinormal mode in that channel. After analytic extraction of the ingoing and outgoing phases, the remaining equations form boundary regular polynomial eigenvalue problems. Their fundamental spectra lift the background coupling degeneracy and reproduce the Schwarzschild spin one and spin two limits of all transverse families. Longitudinal limits instead retain the expected path dependence where local Yang–Mills symmetry is restored; because their local kinetic matrix degenerates as the magnetic background vanishes, we interpret those longitudinal frequencies as fixed multipole reduced spectral resonances. Resolution convergence, independent endpoint recurrences, off grid equation residuals, and Regge–Wheeler and Zerilli regressions validate the resolved spectra. All resolved coupled fundamental families are damped over the sampled frequency and parameter domains; only the decoupled channel carries an analytic mode stability theorem.
This review presents a concise and unified treatment of Wilson lines and Wilson loops in continuum gauge theory, emphasizing their interpretation as parallel transport and their status as gauge covariant transporters and gauge invariant loop observables. Starting from the problem of comparing charged fields at separated points, we derive the path ordered exponential formulation and collect the key kinematical identities: gauge covariance, composition under path concatenation, inversion, and base point dependence. We then explain how local information is encoded in suitable small segment and small loop limits, and how these limits enter reconstruction questions for the underlying gauge connection. Seen as an inverse problem, this perspective clarifies how much of the gauge connection is encoded in loop observables and why traced Wilson loops, while gauge invariant, are intrinsically lossy without additional input. Special attention is given to clarifying common sources of confusion, in particular the distinction between untraced holonomies and traced Wilson loops, and the role of reference path choices when relating open transports to based loop data. The presentation is intended to serve both as an entry point for newcomers and as a compact reference for readers in high energy theory, mathematical physics, and related fields.
ABSTRACT Emergent gravity provides a geometric interpretation of noncommutative gauge theory, in which deformations of a symplectic structure induced by a gauge field are absorbed by diffeomorphisms via the Darboux theorem, giving rise to an effective Riemannian metric. Independently, topological T‐duality identifies pairs of principal torus bundles equipped with distinct geometric and flux data whose associated sigma models are physically equivalent. In this work, we place both constructions within the framework of generalized geometry, thereby enabling a uniform treatment of emergent metrics and T‐duality transformations. We describe emergent gravity in terms of generalized metrics on exact Courant algebroids and interpret the Seiberg–Witten map as a composition of and transformations acting on a flat background. Using the Gualtieri–Cavalcanti formulation of T‐duality as an isomorphism of Courant algebroids, we construct a natural notion of a T‐dual emergent gravity for principal torus bundles. For flat spacetimes with trivial H‐flux, we show that the T‐dual generalized metric again admits an emergent gravity interpretation. At the level of generalized geometry, this result is encoded in a commutative diagram in which T‐duality interchanges the order of the transformations responsible for the emergence of the metric. For general ‐fibrations, we derive explicit formulas for the T‐dual generalized metric and show that the dual background generically carries a nontrivial H‐flux, which obstructs a direct interpretation in terms of conventional symplectic emergent gravity and necessitates an extension of the framework to nonexact Courant algebroids. Our results provide a precise mathematical link between emergent gravity and T‐duality and indicate that generalized geometry furnishes the natural setting for a T‐duality–covariant formulation of emergent gravity, including backgrounds with nonvanishing flux.
ABSTRACT We perform a comprehensive cosmographic analysis of the Rastall gravity extension of the standard model within a spatially flat FLRW framework. We employ the latest observational datasets, including the DR2, cosmic chronometers (CC), and Type Ia supernova samples (PP&SH0ES, Union3, DES‐5yr, and DES‐Dovekie). We constrain the free parameters for the Rastall gravity model using Markov Chain Monte Carlo (MCMC) simulations implemented through the MontePython and CLASS codes, yielding robust and tightly constrained results. Our analysis reveals that the mean value of the Rastall parameter is of order for the DR2+CC dataset and remains consistent with zero at the confidence level, suggesting that the Rastall gravity reduces to the standard general relativity description. For the DR2+CC+PP&SH0ES dataset, the constraint on undergoes a substantial change, reaching the order of and exhibiting a significant departure from general relativity (), also obtain the Hubble constant km , which shows strong agreement with the SH0ES calibration at the confidence level. The cosmographic parameters tend toward and , consistent with the standard cosmological model, while the deceleration parameter lies within the range for both models, confirming accelerated expansion of the universe.
