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Register a new userQuantum $kappa$-Poincare Algebra from de Sitter Space of Momenta
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There is a growing number of physical models, like point particle(s) in 2+1 gravity or Doubly Special Relativity, in which the space of momenta is curved, de Sitter space. We show that for such models the algebra of space-time symmetries possesses a natural Hopf algebra structure. It turns out that this algebra is just the quantum $kappa$-Poincare algebra.
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In this note we study a massive IIA supergravity theory obtained in hep-th/9707139 by compactification of M-theory. We point out that de Sitter space in arbitrary dimensions arises naturally as the vacuum of this theory. This explicitly shows how de Sitter space can be embedded into eleven-dimensional supergravity. In addition we discuss the novel way in which this theory avoids various `no-go theorems which assert that de Sitter space is not a consistent vacua of eleven-dimensional supergravity theory. We also point out that the eight-branes of this theory, which couple electrically to the ten-form, can sweep out de Sitter world-volumes.
We consider a superextension of the extended Jordanian twist, describing nonstandard quantization of anti-de-Sitter ($AdS$) superalgebra $osp(1|4)$ in the form of Hopf superalgebra. The super-Jordanian twisting function and corresponding basic coproduct formulae for the generators of $osp(1|4)$ are given in explicit form. The nonlinear transformation of the classical superalgebra basis not modifying the defining algebraic relations but simplifying coproducts and antipodes is proposed. Our physical application is to interpret the new super-Jordanian deformation of $osp(1|4)$ superalgebra as deformed D=4 $AdS$ supersymmetries. Subsequently we perform suitable contraction of quantum Jordanian $AdS$ superalgebra and obtain new $kappa$-deformation of D=4 Poincare superalgebra, with the bosonic sector describing the light cone $kappa$-deformation of Poincare symmetries.
It is well-known that de Sitter Lie algebra $mathfrak{o}(1,4)$ contrary to anti-de Sitter one $mathfrak{o}(2,3)$ does not have a standard $mathbb{Z}_2$-graded superextension. We show here that the Lie algebra $mathfrak{o}(1,4)$ has a superextension based on the $mathbb{Z}_2timesmathbb{Z}_2$-grading. Using the standard contraction procedure for this superextension we obtain an {it alternative} super-Poincare algebra with the $mathbb{Z}_2timesmathbb{Z}_2$-grading.
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.
Maldacena has shown that the wavefunction of the universe in de Sitter space can be viewed as the partition function of a conformal field theory. In this paper, we investigate this approach to the dS/CFT correspondence in further detail. We emphasize that massive bulk fields are dual to two primary operators on the boundary, which encode information about the two independent behaviors of bulk expectation values at late times. An operator statement of the duality is given, and it is shown that the resulting boundary correlators can be interpreted as transition amplitudes from the Bunch-Davies vacuum to an excited state in the infinite future. We also explain how these scattering amplitudes can be used to compute late-time Bunch-Davies expectation values, and comment on the effects of anomalies in the dual CFT on such expectation values.
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