Abstract
We investigate the structure of conformal Regge trajectories for the maximally supersymmetric (2, 0) theories in six dimensions. The different conformal multiplets in a single superconformal multiplet must all have similarly-shaped Regge trajectories. We show that these super-descendant trajectories interact in interesting ways, leading to new constraints on their shape. For the four-point function of the stress tensor multiplet supersymmetry also softens the Regge behavior in some channels, and consequently we observe that ‘analyticity in spin’ holds for all spins greater than −3. All the physical operators in this correlator therefore lie on Regge trajectories and we describe an iterative scheme where the Lorentzian inversion formula can be used to bootstrap the four-point function. Some numerical experiments yield promising results, with OPE data approaching the numerical bootstrap results for all theories with rank greater than one.
Highlights
All the physical operators in this correlator lie on Regge trajectories and we describe an iterative scheme where the Lorentzian inversion formula can be used to bootstrap the four-point function
We follow the notation of [19] and denote superconformal multiplets as X [p, q]∆, with (∆, ) and [p, q] respectively corresponding to the conformal representation and the so(5) R-symmetry Dynkin labels of the superconformal primary, and with X ∈ {L, A, B, C, D} denoting the type of shortening condition
For short multiplets we do not write ∆ because it is fixed by the other quantum numbers, and we omit for the D-type multiplets because it is always zero
Summary
The advent of Regge theory in the 1960s led to a profound improvement in our understanding of relativistic scattering amplitudes, relating in particular their high-energy behavior to the spectrum of resonances and bound states. The results of [5] indicate that a CFT spectrum organizes itself in Regge trajectories with spectra and OPE coefficients that are smooth functions of the spin This picture elucidates the remarkable smoothness of numerically obtained OPE data, for example that of the three-dimensional Ising model analyzed in [6, 7], and goes some way towards explaining the success of large spin perturbation theory [8, 9], see for example [10, 11]. The form of the superconformal Ward identities and superconformal blocks can be extracted from the more general analysis of [25]
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