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Register a new userQuantum BMS transformations in conformally flat space-times and holography
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We define and study asymptotic Killing and conformal Killing vectors in $d$-dimensional Minkowski, (A)dS, $mathbb{R}times S^{d-1}$ and ${rm AdS}_2times S^{d-2}$. We construct the associated quantum charges for an arbitrary CFT and show they satisfy a closed algebra that includes the BMS as a sub-algebra (i.e. supertranslations and superrotations) plus a novel transformation we call `superdilations. We study representations of this algebra in the Hilbert space of the CFT, as well as the action of the finite transformations obtained by exponentiating the charges. In the context of the AdS/CFT correspondence, we propose a bulk holographic description in semi-classical gravity that reproduces the results obtained from CFT computations. We discuss the implications of our results regarding quantum hairs of asymptotically flat (near-)extremal black holes.
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When two spacetimes are stitched across a null-shell placed at the horizon of a black hole BMS-supertranslation like soldering freedom arises if one demands the induced metric on the horizon shell should remain invariant under the translations generated by the null generators of the shell. We revisit this phenomenon at the horizon of rotating shells and obtain BMS like symmetries. We further show that superrotation like soldering symmetries in the form of conformal isometries can emerge whenever the degenerate metric of any null hypersurface admits a dependency on null (degenerate direction) coordinate. This kind of conformal isometry can also appear for a null surface situated very close to the horizon of black holes. We also study the intrinsic properties of different kinds of horizon shells considered in this note.
We revisit the theory of null shells in general relativity, with a particular emphasis on null shells placed at horizons of black holes. We study in detail the considerable freedom that is available in the case that one solders two metrics together across null hypersurfaces (such as Killing horizons) for which the induced metric is invariant under translations along the null generators. In this case the group of soldering transformations turns out to be infinite dimensional, and these solderings create non-trivial horizon shells containing both massless matter and impulsive gravitational wave components. We also rephrase this result in the language of Carrollian symmetry groups. To illustrate this phenomenon we discuss in detail the example of shells on the horizon of the Schwarzschild black hole (with equal interior and exterior mass), uncovering a rich classical structure at the horizon and deriving an explicit expression for the general horizon shell energy-momentum tensor. In the special case of BMS-like soldering supertranslations we find a conserved shell-energy that is strikingly similar to the standard expression for asymptotic BMS supertranslation charges, suggesting a direct relation between the physical properties of these horizon shells and the recently proposed BMS supertranslation hair of a black hole.
We outline a program for interpreting the higher-spin dS/CFT model in terms of physics in the causal patch of a dS observer. The proposal is formulated in elliptic de Sitter space dS_4/Z_2, obtained by identifying antipodal points in dS_4. We discuss recent evidence that the higher-spin model is especially well-suited for this, since the antipodal symmetry of bulk solutions has a simple encoding on the boundary. For context, we test some other (free and interacting) theories for the same property. Next, we analyze the notion of quantum field states in the non-time-orientable dS_4/Z_2. We compare the physics seen by different observers, with the outcome depending on whether they share an arrow of time. Finally, we implement the marriage between higher-spin holography and observers in dS_4/Z_2, in the limit of free bulk fields. We succeed in deriving an observers operator algebra and Hamiltonian from the CFT, but not her S-matrix. We speculate on the extension of this to interacting higher-spin theory.
Recently it has been shown that infrared divergences in the conventional S-matrix elements of gauge and gravitational theories arise from a violation of the conservation laws associated with large gauge symmetries. These infrared divergences can be cured by using the Faddeev-Kulish (FK) asymptotic states as the basis for S-matrix elements. Motivated by this connection, we study the action of BMS supertranslations on the FK asymptotic states of perturbative quantum gravity. We compute the BMS charge of the FK states and show that it characterizes the superselection sector to which the state belongs. Conservation of the BMS charge then implies that there is no transition between different superselection sectors, hence showing that the FK graviton clouds implement the necessary vacuum transition induced by the scattering process.
We have found that supersymmetry (SUSY) in curved space is broken softly. It is also found that Pauli-Villars regularization preserves the remaining symmetry, softly broken SUSY. Using it we computed the one-loop effective potential along a (classical) flat direction in a Wess-Zumino model in de Sitter space. The analysis is relevant to the Affleck-Dine mechanism for baryogenesis. The effective potential is unbounded from below: $V_{eff}(phi)to -3g^2H^2phi ^2 ln phi ^2 /16pi ^2$, where $phi$ is the scalar field along the flat direction, g is a typical coupling constant, and H is the Hubble parameter. This is identical with the effective potential which is obtained by using proper-time cutoff regularization. Since proper-time cutoff regularization is exact even at the large curvature region, the effective potential possesses softly broken SUSY and reliability in the large curvature region.
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