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Register a new userSpin projection operators in (A)dS and partial masslessness
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We elaborate on the traceless and transverse spin projectors in four-dimensional de Sitter and anti-de Sitter spaces. The poles of these projectors are shown to correspond to partially massless fields. We also obtain a factorisation of the conformal operators associated with gauge fields of arbitrary Lorentz type $(m/2,n/2 )$, with $m$ and $n$ positive integers.
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We elaborate on the spin projection operators in three dimensions and use them to derive a new representation for the linearised higher-spin Cotton tensors.
Starting from the dual Lagrangians recently obtained for (partially) massless spin-2 fields in the Stueckelberg formulation, we write the equations of motion for (partially) massless gravitons in (A)dS in the form of twisted-duality relations. In both cases, the latter admit a smooth flat limit. In the massless case, this limit reproduces the gravitational twisted-duality relations previously known for Minkowski spacetime. In the partially-massless case, our twisted-duality relations preserve the number of degrees of freedom in the flat limit, in the sense that they split into a decoupled pair of dualities for spin-1 and spin-2 fields. Our results apply to spacetimes of any dimension greater than three. In four dimensions, the twisted-duality relations for partially massless fields that appeared in the literature are recovered by gauging away the Stueckelberg field.
A new set of projection operators for three-dimensional models are constructed. Using these operators, an uncomplicated and easily handling algorithm for analysing the unitarity of the aforementioned systems is built up. Interestingly enough, this method converts the task of probing the unitarity of a given 3D system, that is in general a time-consuming work, into a straightforward algebraic exercise; besides, it also greatly clarifies the physical interpretation of the propagating modes. In order to test the efficacy and quickness of the algorithm at hand, the unitarity of some important and timely higher-order electromagnetic (gravitational) systems augmented by both Chern-Simons and higher order Chern-Simons terms are investigated.
The quadratic Casimir operator of the special unitary $SU(N)$ group is used to construct projection operators, which can decompose any of its reducible finite-dimensional representation spaces contained in the tensor product of two and three adjoint spaces into irreducible components. Although the method is general enough, it is specialized to the $SU(2N_f) to SU(2)otimes SU(N_f)$ spin-flavor symmetry group, which emerges in the baryon sector of QCD in the large-$N_c$ limit, where $N_f$ and $N_c$ are the numbers of light quark flavors and color charges, respectively. The approach leads to the construction of spin and flavor projection operators that can be implemented in the analysis of the $1/N_c$ operator expansion. The use of projection operators allows one to successfully project out the desired components of a given operator and subtract off those that are not needed. Some explicit examples in $SU(2)$ and $SU(3)$ are detailed.
The $Tbar T$ deformation of a conformal field theory has a dual description as a cutoff $AdS_3$ spacetime, at least at the level of pure 3d gravity. We generalize this deformation in such a way that it builds up a patch of bulk $dS_3$ spacetime instead. At each step along the trajectory in the space of $2d$ theories, the theory is deformed by a specific combination of $Tbar T$ and the two-dimensional cosmological constant. This provides a concrete holographic dual for the warped throat on the gravity side of the dS/dS duality, at leading order in large central charge. We also analyze a sequence of excitations of this throat on both sides of the duality, as well as the entanglement entropy. Our results point toward a mechanism for obtaining de Sitter solutions starting from seed conformal field theories with AdS duals.
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