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Register a new userNon-conformal supercurrents in six dimensions
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Non-conformal supercurrents in six dimensions are described, which contain the trace of the energy-momentum tensor and the gamma-trace of the supersymmetry current amongst their component fields. Within the superconformal approach to ${cal N} = (1, 0)$ supergravity, we present various distinct non-conformal supercurrents, one of which is associated with an ${cal O}(2)$ (or linear) multiplet compensator, while another with a tensor multiplet compensator. We also derive an infinite class of non-conformal supercurrents involving ${cal O}(n)$ multiplets with $n > 2$. As an illustrative example we construct the relaxed hypermultiplet in supergravity. Finally, we put forward a non-conformal supercurrent in the ${cal N} = (2, 0)$ supersymmetric case.
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In this article, we continue the investigation of hep-th 1611.02179 regarding iterative properties of dual conformal integrals in higher dimensions. In d=4, iterative properties of four and five point dual conformal integrals manifest themselves in the famous BDS ansatz conjecture. In hep-th 1611.02179 it was also conjectured that a similar structure of integrals may reappear in d=6. We show that one can systematically, order by order in the number of loops, construct combinations of d=6 integrals with 1/(p^2)^2 propagators with an iterative structure similar to the d=4 case. Such combinations as a whole also respect dual conformal invariance but individual integrals may not.
Massless conformal scalar field in six dimensions corresponds to the minimal unitary representation (minrep) of the conformal group SO(6,2). This minrep admits a family of deformations labelled by the spin t of an SU(2)_T group, which is the 6d analog of helicity in four dimensions. These deformations of the minrep of SO(6,2) describe massless conformal fields that are symmetric tensors in the spinorial representation of the 6d Lorentz group. The minrep and its deformations were obtained by quantization of the nonlinear realization of SO(6,2) as a quasiconformal group in arXiv:1005.3580. We give a novel reformulation of the generators of SO(6,2) for these representations as bilinears of deformed twistorial oscillators which transform nonlinearly under the Lorentz group SO(5,1) and apply them to define higher spin algebras and superalgebras in AdS_7. The higher spin (HS) algebra of Fradkin-Vasiliev type in AdS_7 is simply the enveloping algebra of SO(6,2) quotiented by a two-sided ideal (Joseph ideal) which annihilates the minrep. We show that the Joseph ideal vanishes identically for the quasiconformal realization of the minrep and its enveloping algebra leads directly to the HS algebra in AdS_7. Furthermore, the enveloping algebras of the deformations of the minrep define a discrete infinite family of HS algebras in AdS_7 for which certain 6d Lorentz covariant deformations of the Joseph ideal vanish identically. These results extend to superconformal algebras OSp(8*|2N) and we find a discrete infinite family of HS superalgebras as enveloping algebras of the minimal unitary supermultiplet and its deformations. Our results suggest the existence of a discrete family of (supersymmetric) HS theories in AdS_7 which are dual to free (super)conformal field theories (CFTs) or to interacting but integrable (supersymmetric) CFTs in 6d.
The a-function is a proposed quantity defined in even dimensions which has a monotonic behaviour along RG flows, related to the beta-functions via a gradient flow equation. We study the a-function for a general scalar theory in six dimensions, using the beta-functions up to three-loop order for both the MSbar and MOM schemes (the latter presented here for the first time at three loops).
The supersymmetrization of curvature squared terms is important in the study of the low-energy limit of compactified superstrings where a distinguished role is played by the Gauss-Bonnet combination, which is ghost-free. In this letter, we construct its off-shell ${cal N} = (1, 0)$ supersymmetrization in six dimensions for the first time. By studying this invariant together with the supersymmetric Einstein-Hilbert term we confirm and extend known results of the $alpha$-corrected string theory compactified to six dimensions. Finally, we analyze the spectrum about the ${rm AdS}_3times{rm S}^3$ solution.
In search of non-trivial field theories in high dimensions, we study further the tensor representation of the $O(N)$-symmetric $phi^4$ field theory introduced by Herbut and Janssen (Phys. Rev. D. 93, 085005 (2016)), by using four-loop perturbation theory in two cubic interaction coupling constants near six dimensions. For infinitesimal values of the parameter $epsilon=(6-d)/2$ we find infrared-stable fixed point with two relevant quadratic operators for $N$ within the conformal windows $1<N<2.653$ and $2.999<N<4$, and compute critical exponents at this fixed point to the order $epsilon^4$. Taking the four-loop beta-functions at their face value we determine the higher-order corrections to the edges of the above conformal windows at finite $epsilon$, to find both intervals to shrink to zero above $epsilonapprox 0.15$. The disappearance of the conformal windows with the increase of $epsilon$ is due to the collision of the Wilson-Fisher $mathcal{O}(epsilon)$ infrared fixed point with the $mathcal{O}(1)$ mixed-stable fixed point that appears at two and persists at higher loops. The latter may be understood as a Banks-Zaks type fixed point that becomes weakly coupled near the right edge of either conformal window. The consequences and issues raised by such an evolution of the flow with dimension are discussed. It is also shown both within the perturbation theory and exactly that the tensor representation at $N=3$ and right at the $mathcal{O}(epsilon)$ infrared-stable fixed point exhibits an emergent $U(3)$ symmetry. A role of this enlarged symmetry in possible protection of the infrared fixed point at $N=3$ is noted.
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