Nonlinear dynamics of flux compactification

We study the nonlinear evolution of unstable flux compactifications, applying numerical relativity techniques to solve the Einstein equations in D dimensions coupled to a q-form field and positive cosmological constant. We show that initially homogeneous flux compactifications are unstable to dynamically forming warped compactifications. In some cases, we find that the warping process can serve as a toy-model of slow-roll inflation, while in other instances, we find solutions that eventually evolve to a singular state. Analogous to dynamical black hole horizons, we use the geometric properties of marginally trapped surfaces to characterize the lower dimensional vacua in the inhomogeneous and dynamical settings we consider. We find that lower-dimensional vacua with a lower expansion rate are dynamically favoured, and in some cases find spacetimes that undergo a period of accelerated expansion followed by contraction.

Kalb-Ramond backgrounds in α′-complete cosmology

We study the matter-coupled equations of motion for cosmological NS massless fields including all α′ corrections in an O(d, d) duality invariant approach, with emphasis on the Kalb-Ramond two-form field B(2) and its source. Solutions for the vacuum and matter cases are found and the corresponding Einstein frame cosmologies are discussed. We also show that the ansatz for B(2) required by the duality invariant framework implies that the two-form is non-isotropic.

A non-relativistic limit of NS-NS gravity

We discuss a particular non-relativistic limit of NS-NS gravity that can be taken at the level of the action and equations of motion, without imposing any geometric constraints by hand. This relies on the fact that terms that diverge in the limit and that come from the Vielbein in the Einstein-Hilbert term and from the kinetic term of the Kalb-Ramond two-form field cancel against each other. This cancelling of divergences is the target space analogue of a similar cancellation that takes place at the level of the string sigma model between the Vielbein in the kinetic term and the Kalb-Ramond field in the Wess-Zumino term. The limit of the equations of motion leads to one equation more than the limit of the action, due to the emergence of a local target space scale invariance in the limit. Some of the equations of motion can be solved by scale invariant geometric constraints. These constraints define a so-called Dilatation invariant String Newton-Cartan geometry.

An improved holographic nodal line semimetal

We study an improved holographic model for the strongly coupled nodal line semimetal which satisfies the duality relation between the rank two tensor operators $$ \overline{\psi}{\gamma}^{\mu v}\psi $$ ψ ¯ γ μv ψ and $$ \overline{\psi}{\gamma}^{\mu v}{\gamma}^5\psi $$ ψ ¯ γ μv γ 5 ψ . We introduce a Chern-Simons term and a mass term in the bulk for a complex two form field which is dual to the above tensor operators and the duality relation is automatically satisfied from holography. We find that there exists a quantum phase transition from a topological nodal line semimetal phase to a trivial phase. In the topological phase, there exist multiple nodal lines in the fermionic spectrum which are topologically nontrivial. The bulk geometries are different from the previous model without the duality constraint, while the resulting properties are qualitatively similar to those in that model. This improved model provides a more natural ground to analyze transports or other properties of strongly coupled nodal line semimetals.

Dynamical system analysis of self-interacting three-form field cosmological model: stability and bifurcation

The present work deals with Cosmological model of a three-form field, minimally coupled to gravity and interacting with cold dark matter in the background of flat FLRW space-time. By suitable choice of the dimensionless variables, the evolution equations are converted to an autonomous system and cosmological study is done by dynamical system analysis. The critical points are determined and the stability of the (non-hyperbolic) equilibrium points are examined by center manifold Theory. Possible bifurcation scenarios have been examined by the Poincaré index theory to identify possible cosmological phase transition. Also stabilities of the critical points have been analyzed globally using geometric features.

Seiberg-Witten map for D-branes in large R-R field background

We obtain a Seiberg-Witten map for the gauge sector of multiple Dp-branes in a large R-R (p − 1)-form field background up to the first-order in the inverse R-R field background. By applying the Seiberg-Witten map and then electromagnetic duality on the non-commutative D3-brane theory in the large R-R 2-form background, we find the expected commutative diagram of the Seiberg-Witten map and electromagnetic duality. Extending the U(1) gauge group to the U(N) gauge group, we obtain a commutative description of the D-branes in the large R-R field background. This construction is different from the known result.

Regular black hole interior spacetime supported by three-form field

In this paper, we show that a minimally coupled 3-form endowed with a proper potential can support a regular black hole interior. By choosing an appropriate form for the metric function representing the radius of the 2-sphere, we solve for the 3-form field and its potential. Using the obtained solution, we construct an interior black hole spacetime which is everywhere regular. The singularity is replaced with a Nariai-type spacetime, whose topology is $$\text {dS}_2 \times \text {S}^2$$ dS 2 × S 2 , in which the radius of the 2-sphere is constant. So long as the interior continues to expand indefinitely, the geometry becomes essentially compactified. The 2-dimensional de Sitter geometry appears despite the negative potential of the 3-form field. Such a dynamical compactification could shed some light on the origin of de Sitter geometry of our Universe, exacerbated by the Swampland conjecture. In addition, we show that the spacetime is geodesically complete. The geometry is singularity-free due to the violation of the null energy condition.

Static spherically symmetric three-form stars

We consider interior static and spherically symmetric solutions in a gravity theory that extends the standard Hilbert–Einstein action with a Lagrangian constructed from a three-form field $$A_{\alpha \beta \gamma }$$ A α β γ , which generates, via the field strength and a potential term, a new component in the total energy-momentum tensor of the gravitational system. We formulate the field equations in Schwarzschild coordinates and investigate their solutions numerically for different equations of state of neutron and quark matter, by assuming that the three-field potential is either a constant or possesses a Higgs-like form. Moreover, stellar models, described by the stiff-fluid, radiation-like, bag model and the Bose–Einstein condensate equations of state are explicitly obtained in both general relativity and three-form gravity, thus allowing an in-depth comparison between the astrophysical predictions of these two gravitational theories. As a general result we find that, for all the considered equations of state, three-form field stars are more massive than their general relativistic counterparts. As a possible astrophysical application, we suggest that the 2.5$$ M_{\odot }$$ M ⊙ mass compact object, associated with the GW190814 gravitational wave event, could be in fact a neutron or a quark star described by the three-form gravity theory.

Geometric Justification of the Fundamental Interaction Fields for the Classical Long-Range Forces

Based on the principle of reparametrization invariance, the general structure of physically relevant classical matter systems is illuminated within the Lagrangian framework. In a straightforward way, the matter Lagrangian contains background interaction fields, such as a 1-form field analogous to the electromagnetic vector potential and symmetric tensor for gravity. The geometric justification of the interaction field Lagrangians for the electromagnetic and gravitational interactions are emphasized. The generalization to E-dimensional extended objects (p-branes) embedded in a bulk space M is also discussed within the light of some familiar examples. The concept of fictitious accelerations due to un-proper time parametrization is introduced, and its implications are discussed. The framework naturally suggests new classical interaction fields beyond electromagnetism and gravity. The simplest model with such fields is analyzed and its relevance to dark matter and dark energy phenomena on large/cosmological scales is inferred. Unusual pathological behavior in the Newtonian limit is suggested to be a precursor of quantum effects and of inflation-like processes at microscopic scales.

Consistency conditions for p-form field localization on codimension two braneworlds

In a recent work (Eur. Phys. J. C 80(5), 432, 2020), the present authors obtained general stringent conditions on the localization of fields in braneworlds by imposing the requirement that its zero mode must satisfy Einstein’s equations (EEs). In this manuscript, we continue this study by considering free p-form fields. These fields present an on-shell equivalency relation between a p-form and a $$(D-p-2)$$ ( D - p - 2 ) -form, provided by a Hodge duality (HD) transformation. This symmetry will impose a new consistency condition, namely, confinement of a p-form on the brane must imply the localization of its dual. We apply the above two conditions to 6D braneworld models. With this, we find that in global string-like defects, for example, the 1-form field has a normalizable zero mode. By using the HD as a guide, we show that its bulk dual 3-form field also has a normalizable zero mode, making the confinement consistent with HD. However, these solutions cannot be made consistent with EE, therefore, these fields must be ruled out. In fact, by imposing both conditions, only the scalar field and its dual can be consistently localized in codimension two braneworlds. In this way, all the literature so far in which the free vector field (1-form) is localized in codimension two models should be reviewed. These results also point to the fact that the symmetries of the fields can be used to verify the consistency of their localization and even prohibit it.