Abstract
We construct an open string theory whose single-trace part of the tree-level S-matrix reproduces the S-matrix of the ABJ(M) theory with a unitary gauge group. We also demonstrate that the multi-trace part of the string theory tree-level S-matrix — which has no counterpart in the pure $ \mathcal{N} $ = 6 super-Chern-Simons theory — is due to conformal supergravity interactions and identify certain Lagrangian interaction terms. Our construction suggests that there exists a higher dimensional theory which can be dimensionally-reduced, in a certain sense, to the ABJ(M) theory. It also suggests a generalization of this theory to product gauge groups with more than two factors.
Highlights
The three-dimensional ABJ(M) theory [16] shares many of the properties of N = 4 sYM theory such as the integrability of the planar dilatation operator [17, 18] and invariance of its tree-level amplitudes and of its loop integrands under the Yangian of the superconformal group [19,20,21]
We demonstrate that the multi-trace part of the string theory tree-level S-matrix — which has no counterpart in the pure N = 6 super-Chern-Simons theory — is due to conformal supergravity interactions and identify certain Lagrangian interaction terms
It was suggested that the scattering amplitudes of this theory have a Grassmannian formulation [22] as well as a formulation [23] exhibiting holomorphic localization on curves of a certain degree in twistor space,2 which in turn suggests that a twistor string theory may exist for this theory as well
Summary
The supertwistors for the N -extended three-dimensional superconformal group OSp(N |4, R) were discussed in detail in [39]; they are given by the pairs (ξμ, ηA) where the two components transform in the fundamental representations of Sp(4) and SO(N ), respectively. From a bosonic point of view we shall construct a string theory with target space (z, y) and impose the identification as a specific choice of asymptotic state kinematics. While this string theory has the complete SU(3, 2) symmetry, vertex operators for the restricted states do not as the additional μ3 direction is treated separately. To the discussion in [13, 15], this restricts the possible gauge symmetry of the target space effective theory This cancellation is unimportant and we can pick any desired numbers N /M of fermions. It would be interesting to analyze their structure and understand whether or not it is a standard field theory.
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