Twistor constructions for higher-spin extensions of (self-dual) Yang-Mills

We present the inverse Penrose transform (the map from spacetime to twistor space) for self-dual Yang-Mills (SDYM) and its higher-spin extensions on a flat background. The twistor action for the higher-spin extension of SDYM (HS-SDYM) is of $$ \mathcal{BF} $$ BF -type. By considering a deformation away from the self-dual sector of HS-SDYM, we discover a new action that describes a higher-spin extension of Yang-Mills theory (HS-YM). The twistor action for HS-YM is a straightforward generalization of the Yang-Mills one.

Kerr–Schild metrics in teleparallel gravity

We show that the Kerr–Schild ansatz can be extended from the metric to the tetrad, and then to teleparallel gravity where curvature vanishes but torsion does not. We derive the equations of motion for the Kerr–Schild null vector, and describe the solution for a rotating black hole in this framework. It is shown that the solution depends on the chosen tetrad in a non-trivial way if the spin connection is fixed to be the one of the flat background spacetime. We show furthermore that any Kerr–Schild solution with a flat background is also a solution of $$f({\mathcal {T}})$$ f ( T ) gravity.

Construction of Higher-Order Metric Fluctuation Terms in Spacetime Symmetry-Breaking Effective Field Theory

We examined the basic conservation laws for diffeomorphism symmetry in the context of spontaneous diffeomorphism and local Lorentz-symmetry breaking. The conservation laws were used as constraints on a generic series of terms in an expansion around a flat background. We found all such terms for a two-tensor coupling to cubic order in the metric and tensor field fluctuations. The results are presented in a form that can be used for phenomenological calculations. One key result is that if we preserve the underlying diffeomorphism symmetry in a spontaneous-symmetry breaking scenario, one cannot decouple the two-tensor fluctuations from the metric fluctuations at the level of the action, except in special cases of the quadratic actions.

Background mode selection during asymptotic-de Sitter inflation

For the first time, we choose non-flat vacuum mode for background spacetime based on the minimum number of created particles during early non-de Sitter inflation. In conventional methods for calculating the number of created particles, the flat background is selected automatically and causes a negative number problem for created particles during asymptotic-de Sitter inflation. In a covariant approach to curved spacetime, both real and background spacetimes should be selected, curved and consequently the relation for particle creation should be modify. As an interesting finding from this research, flat space does not include minimum number of particles and there are some asymptotic de Sitter spacetimes with fewer number. Therefore, in the generalized formula for particle creation, we choose a non-flat background containing the minimum number of created particles.

Conceptual Pitfalls in Teaching the Linearized Approximation in Introductory General Relativity

The decomposition of the metric tensor into a flat background plus small perturbations used in linearized general relativity is often a source of confusion for the student because these two parts are only Lorentz-invariant but not generally covariant. The underlying, crucial, conceptual switch from a dynamical gravitational field to a test field on a fixed background is often omitted in presenting this course material. This issue is clarified and an improved presentation is proposed.

New locally (super)conformal gauge models in Bach-flat backgrounds

For every conformal gauge field $$ {h}_{\alpha (n)\overset{\cdot }{\alpha }(m)} $$ h α n α ⋅ m in four dimensions, with n ≥ m > 0, a gauge-invariant action is known to exist in arbitrary conformally flat backgrounds. If the Weyl tensor is non-vanishing, however, gauge invariance holds for a pure conformal field in the following cases: (i) n = m = 1 (Maxwell’s field) on arbitrary gravitational backgrounds; and (ii) n = m + 1 = 2 (conformal gravitino) and n = m = 2 (conformal graviton) on Bach-flat backgrounds. It is believed that in other cases certain lower-spin fields must be introduced to ensure gauge invariance in Bach-flat backgrounds, although no closed-form model has yet been constructed (except for conformal maximal depth fields with spin s = 5/2 and s = 3). In this paper we derive such a gauge-invariant model describing the dynamics of a conformal gauge field $$ {h}_{\alpha (3)\overset{\cdot }{\alpha }} $$ h α 3 α ⋅ coupled to a self-dual two-form. Similar to other conformal higher-spin theories, it can be embedded in an off-shell superconformal gauge-invariant action. To this end, we introduce a new family of $$ \mathcal{N} $$ N = 1 superconformal gauge multiplets described by unconstrained prepotentials ϒα(n), with n > 0, and propose the corresponding gauge-invariant actions on conformally-flat backgrounds. We demonstrate that the n = 2 model, which contains $$ {h}_{\alpha (3)\overset{\cdot }{\alpha }} $$ h α 3 α ⋅ at the component level, can be lifted to a Bach-flat background provided ϒα(2) is coupled to a chiral spinor Ωα. We also propose families of (super)conformal higher-derivative non-gauge actions and new superconformal operators in any curved space. Finally, through considerations based on supersymmetry, we argue that the conformal spin-3 field should always be accompanied by a conformal spin-2 field in order to ensure gauge invariance in a Bach-flat background.

The color appearance of three-dimensional, curved, transparent objects

Studies on the perceived color of transparent objects have elucidated potential mechanisms but have mainly focused on flat filters that overlay a flat background. However, studies with flat filters have not captured all aspects of physical transparency, such as caustics, specular reflections/highlights, and shadows. Here, we investigate color matching experiments with three-dimensional transparent objects for different matching stimuli: a uniform patch and a flat filter overlaying a variegated background. Two different instructions were given to observers: change the color of the matching stimulus until it has the same color as the transparent object (for the patch and flat filter) or until it has the same color as the dye that was used to tint the transparent object (for the patch). Regardless of instruction or matching element, observers match the mean chromaticity of the glass object, but the luminance of matches depends on the backgrounds of the test image and the matching element, indicating that a color constancy-esque discounting operation is at work. We applied three models from flat filter studies to see if they generalize to our stimuli: the convergence model and the ratio of either the means (RMC) or standard deviations (RSD) of cone excitations. The convergence model does not generalize to our stimuli, but the RMC generalizes to a wider range of stimuli than the RSD. However, there is an edge case where RMC also breaks down and there may be additional features that trade-off with RMC when observers match the color of thick, curved transparent objects.

Relating Noncommutative SO(2,3)☆ Gravity to the Lorentz-Violating Standard-Model Extension

We consider a model of noncommutative gravity that is based on a spacetime with broken local SO(2,3) ☆ symmetry. We show that the torsion-free version of this model is contained within the framework of the Lorentz-violating Standard-Model Extension (SME). We analyze in detail the relation between the torsion-free, quadratic limits of the broken SO(2,3) ☆ model and the Standard-Model Extension. As part of the analysis, we construct the relevant geometric quantities to quadratic order in the metric perturbation around a flat background.