Abstract
We continue our investigation of Z-theory, the second double-copy component of open-string tree-level interactions besides super-Yang-Mills (sYM). We show that the amplitudes of the extended non-linear sigma model (NLSM) recently considered by Cachazo, Cha, and Mizera are reproduced by the leading α′-order of Z-theory amplitudes in the semi-abelian case. The extension refers to a coupling of NLSM pions to bi-adjoint scalars, and the semi-abelian case involves to a partial symmetrization over one of the color orderings that characterize the Z-theory amplitudes. Alternatively, the partial symmetrization corresponds to a mixed interaction among abelian and non-abelian states in the underlying open-superstring amplitude. We simplify these permutation sums via monodromy relations which greatly increase the efficiency in extracting the α′-expansion of these amplitudes. Their α′-corrections encode higher-derivative interactions between NLSM pions and bi-colored scalars all of which obey the duality between color and kinematics. Through double-copy, these results can be used to generate the predictions of supersymmetric Dirac-Born-Infeld-Volkov-Akulov theory coupled with sYM as well as a complete tower of higher-order α′-corrections.
Highlights
Its amplitudes to be the set of doubly-ordered functions Zσ(τ ) of ref. [7] — iterated integrals over the boundary of a worldsheet of disk topology — which arise in the tree-level amplitudes of the open superstring [8, 9]
The extension refers to a coupling of non-linear sigma model (NLSM) pions to bi-adjoint scalars, and the semi-abelian case involves to a partial symmetrization over one of the color orderings that characterize the Z-theory amplitudes
Unlike sYM where color and kinematics, along with their respective Lie-algebra structures, can be cleanly separated, the α′dependent kinematic factors of color-stripped semi-abelian Z-theory involve functions of both CP traces and momenta. Each of these orders in α′ can be understood as part of a successive set of color-kinematic satisfying effective field theories, whose culmination in Z-theory exhibits very soft UV behavior
Summary
He we provide a lightening overview of doubly-ordered Z-theory amplitudes so as to set up the main results. Intertwine the contributions from different integration domains resulting in an (n−3)!-basis at fixed integrand ordering τ. Perhaps the most natural way to think about Z-theory as an effective field theory is as a doubly-colored scalar theory where one color (corresponding to color order σ, whose generators we will annotate with ta) is provided by the stringy CP factors. (corresponding to color order τ , whose generators we will annotate with T a) represents a familiar field-theory non-abelian color dressing. We will derive simplified representations for the CP dressed Z-amplitudes (2.6) when some of the generators ta are abelian In this semi-abelian case, the open-string amplitudes (2.7) encode a UV completion of supersymmetric DBIVA coupled with sYM [50], and our subsequent results on Z(.
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