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Action principles for the single and double valued continuous-spin representations of the Poincare group have been recently proposed in a Segal-like formulation. We address three related issues: First, we explain how to obtain these actions directly from the Fronsdal-like and Fang-Fronsdal-like equations by solving the traceless constraints in Fourier space. Second, we introduce a current, similar to the one of Berends, Burgers and Van Dam, which is bilinear in a pair of scalar matter fields, to which the bosonic continuous-spin field can couple minimally. Third, we investigate the current exchange mediated by a continuous-spin particle obtained from this action principle and investigate whether it propagates the right degrees of freedom, and whether it reproduces the known result for massless higher-spin fields in the helicity limit.
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Classical results and recent developments on the theoretical description of elementary particles with continuous spin are reviewed. At free level, these fields are described by unitary irreducible representations of the isometry group (either Poincare or anti de Sitter group) with an infinite number of physical degrees of freedom per spacetime point. Their basic group-theoretical and field-theoretical descriptions are reviewed in some details. We mention a list of open issues which are crucial to address for assessing their physical status and potential relevance.
Gauge/Gravity duality as a theory of matter needs a systematic way to characterise a system. We suggest a `dimensional lifting of the least irrelevant interaction to the bulk theory. As an example, we consider the spin-orbit interaction, which causes magneto-electric interaction term. We show that its lifting is an axionic coupling. We present an exact and analytic solution describing diamagnetic response. Experimental data on annealed graphite shows a remarkable similarity to our theoretical result. We also find an analytic formulas of DC transport coefficients, according to which, the anomalous Hall coefficient interpolates between the coherent metallic regime with $rho_{xx}^{2}$ and incoherent metallic regime with $rho_{xx}$ as we increase the disorder parameter $beta$. The strength of the spin-orbit interaction also interpolates between the two scaling regimes.
One of the most important mathematical tools necessary for Quantum Field Theory calculations is the field propagator. Applications are always done in terms of plane waves and although this has furnished many magnificent results, one may still be allowed to wonder what is the form of the most general propagator that can be written. In the present paper, by exploiting what is called polar form, we find the most general propagator in the case of spinors, whether regular or singular, and we give a general discussion in the case of vectors.
AdS dynamics for massive scalar field is studied both by solving exactly the equation of motion and by constructing bulk-boundary propagator. A Robertson-Walker-like metric is deduced from the familiar SO(2,n) invariant metric. The metric allows us to present a time-like Killing vector, which is not only invariant under space-like transformations but also invariant under the isometric transformations of SO(2,n) in certain sense. A horizon appears in this coordinate system. Singularities of field variables at boundary are demonstrated explicitly. It is shown that there is a one-to-one correspondence among the exact solutions and the bulk fields obtained by using the bulk-boundary propagator.
We propose a description of %manifestly supersymmetric continuous spin representations in $4D,mathcal{N}=1$ Minkowski superspace at the level of equations of motions. The usual continuous spin wave function is promoted to a chiral or a complex linear superfield which includes both the single-valued (span integer helicities) and the double-valued (span half-integer helicities) representations thus making their connection under supersymmetry manifest. The set of proposed superspace constraints for both superfield generate the expected Wigners conditions for both representations.
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