Maxwell's equations are invariant under both duality rotations and conformal transformations. Recently Bandos, Lechner, Sorokin, and Townsend have found a nonlinear generalisation of electrodynamics which possesses both of these symmetries. We couple this theory to General Relativity and explore self-gravitating configurations with a clear physical interpretation. We find charged black holes and exact gravitational waves. The black hole geometry is Reissner-Nordström, however, the non-linearity parameter acts as a screening factor allowing extremal configurations where the mass of the black hole is smaller than its charge. Furthermore, we also discuss the phenomenon of birefringence and determine the optical metrics associated to the propagation of photons.
We present a conformal isometry for static extremal black hole solutions in all four-dimensional Einstein-Maxwell-scalar theories with electromagnetic duality groups `of type $E_7$'. This includes, but is not limited to, all supergravity theories with $\mathcal{N}>2$ supersymmetry and all $\mathcal{N}=2$ supergravity theories with symmetric scalar manifolds. The conformal isometry is valid for arbitrary electromagnetic charge configurations and relies crucially on the notion of Freudenthal duality.
In this paper we obtain exact asymptotically anti-de Sitter black hole solutions and asymptotically Lifshitz black hole solutions with dynamical exponents $z=0$ and $z=4$ of four-dimensional conformal gravity coupled with a self-interacting conformally invariant scalar field. Then, we compute their thermodynamical quantities, such as the mass, the Wald entropy and the Hawking temperature. The mass expression is obtained by using the generalized off-shell Noether potential formulation. It is found that the anti-de Sitter black holes as well as the Lifshitz black holes with $z=0$ have zero mass …
We use conformal symmetry to constrain the shape of inflationary correlators in the presence of long-lived vector field perturbations. Applying conformal Ward identities, we derive general expressions, up to amplitudes and normalization factors, for the two and three point correlators in the presence of vector fields mediated by the interaction $f(ϕ)\left(F_{μν}F^{μν}+α\tilde{F}_{μν}F^{μν}\right)$, where $f(ϕ)$ is a suitable coupling function between the scalar and the vector field. The previous interaction allows for isotropy and parity symmetry breaking and is consistent with super horizon c…
A geometric torsion (GT) underlying a $2$-form in a $(4$$+$$1)$-dimensional $U(1)$ gauge theory is revisited with a renewed perspective for a non-perturbation (NP) gravity in $d$$=$$4$. In the context we provide evidences to a holographic correspondence between a bulk GT and a boundary NP gravity. Interestingly the Killing symmetries in General Relativity (GR) are shown to provide a subtle clue to the quantum gravity. The NP gravity is shown to incorporate a $(B_{2}$$ \wedge $$F_{2})$ coupling, sourced by a non-Newtonian potential, to an exact geometry in GR. Remarkably the NP correction is id…
We deal with the duality symmetry of the Dilaton field in cosmology and specifically with the so-called Gasperini-Veneziano duality transformation. In particular, we determine two conformal equivalent theories to the Dilaton field, and we show that under conformal transformations Gasperini-Veneziano duality symmetry does not survive. Moreover, we show that those theories share a common conservation law, of Noetherian kind, while the symmetry vector which generates the conservation law is an isometry only for the Dilaton field. Finally, we show that the Lagrangian of the Dilaton field is equiva…
We show that a $3d$ sourced conformal Carrollian field theory has the right kinematic properties to holographically describe gravity in $4d$ asymptotically flat spacetime. The external sources encode the leaks of gravitational radiation at null infinity. The Ward identities of this theory are shown to reproduce those of the $2d$ celestial CFT after relating Carrollian to celestial operators. This suggests a new set of interplays between gravity in asymptotically flat spacetime, sourced conformal Carrollian field theory and celestial CFT.
Under two separate symmetry assumptions, we demonstrate explicitly how the equations governing a general anti-self-dual conformal structure in four dimensions can be reduced to the Manakov-Santini system, which determines the three-dimensional Einstein-Weyl structure on the space of orbits of symmetry. The two symmetries investigated are a non-null translation and a homothety, which are previously known to reduce the second heavenly equation to the Laplace's equation and the hyper-CR system, respectively. Reductions on the anti-self-dual null-Kähler condition are also explored in both cases.
We employ holographic duality to compute $\langle T_{μν} \rangle$ in strongly coupled $\mathcal N = 4$ supersymmetric Yang-Mills theory and then study evolution of the semiclassical Einstein field equations sourced by $\langle T_{μν} \rangle$. Linearizing about de Sitter space, we find that the semiclassical equations of motion reduce to a four dimensional scalar wave equation coupled to a five dimensional scalar wave equation. We compute the mode spectrum of these equations and find that there exists a critical value of the Hubble constant $H_c$ for which de Sitter space is unstable when $H <…
We consider averaged null energy conditions (ANEC) for strongly coupled quantum field theories in even (two and four) dimensional curved spacetimes by applying the no-bulk-shortcut principle in the context of the AdS/CFT duality. In the same context but in odd-dimensions, the present authors previously derived a conformally invariant averaged null energy condition (CANEC), which is a version of the ANEC with a certain weight function for conformal invariance. In even-dimensions, however, one has to deal with gravitational conformal anomalies, which make relevant formulas much more complicated …
We show that the extreme six-dimensional black string admits a conformal isometry under inversion. Duality relations between null geodesics of various brane geometries are demonstrated, some of which have a geometrical origin through an optical metric.
According to more recent AdS/CFT interpretation \cite{Karch:2015rpa}, in which varying cosmological constant $Λ$ in the bulk corresponds to varying the curvature radius governing the space on which the field theory resides, we study the criticality of thermodynamic curvatures for thermal boundary conformal field theories (CFT) that are dual to $d$-dimensional charged anti-de Sitter (AdS) black holes, embedded in $D$-dimensional M-theory/superstring inspired models having $AdS_{d}\times \mathbb{S}^{d+k}$ spacetime with $D=2d+k$. Analogous with criticality features acquired for charged AdS black…
We examine the achronal averaged null energy condition~(ANEC) for a class of conformal field theories~(CFT) at strong coupling in curved spacetime. By applying the AdS/CFT duality, we find holographic models which violate the achronal ANEC for $3+1$ and $4+1$-dimensional boundary theories. In our model, the bulk spacetime is an asymptotically AdS vacuum bubble solution with neither causality violation nor singularities. The conformal boundary of our bubble solution is asymptotically flat and is causally proper in the sense that a "fastest null geodesics" connecting any two points on the bounda…
