Semi-abelian Z-theory: NLSM+$\phi$$^3$ from the open string

Joseph M. Carrasco (1) , Carlos R. Mafra (2) , Oliver Schlotterer (3)

1 IPHT - Institut de Physique Théorique - UMR CNRS 3681
2 University of Southampton
3 AEI - Max-Planck-Institut für Gravitationsphysik ( Albert-Einstein-Institut )

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 $\alpha$'-order of Z-theory amplitudes in the semi-abelian limit. The extension refers to a coupling of NLSM pions to bi-adjoint scalars, and the semi-abelian limit refers 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 $\alpha$'-expansion of these amplitudes. Their $\alpha$'-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 $\alpha$'-corrections.

Domaines: Physique [physics]

Joseph M. Carrasco, Carlos R. Mafra, Oliver Schlotterer. Semi-abelian Z-theory: NLSM+$\phi$$^3$ from the open string. 2017. ⟨cea-01529959⟩