Higher-loop amplitude monodromy relations in string and gauge theory.

Piotr Tourkine (1) , P. Vanhove (2)

1 DAMTP - Department of Applied Mathematics and Theoretical Physics
2 IPHT - Institut de Physique Théorique - UMR CNRS 3681

The monodromy relations in string theory provide a powerful and elegant formalism to understand some of the deepest properties of tree-level field theory amplitudes, like the color-kinematics duality. This duality has been instrumental in tremendous progress on the computations of loop amplitudes in quantum field theory, but a higher-loop generalisation of the monodromy construction was lacking. In this letter, we extend the monodromy relations to higher loops in open string theory. Our construction, based on a contour deformation argument of the open string diagram integrands, leads to new identities that relate planar and non-planar topologies in string theory. We write one and two-loop monodromy formulae explicitly at any multiplicity. In the field theory limit, at one-loop we obtain identities that reproduce known results. At two loops, we check our formulae by unitarity in the case of the four-point N = 4 super-Yang-Mills amplitude.

Domaines: Physique des Hautes Energies - Théorie [hep-th]

Piotr Tourkine, P. Vanhove. Higher-loop amplitude monodromy relations in string and gauge theory.. Physical Review Letters, 2016, 117, pp.211601. ⟨10.1103/PhysRevLett.117.211601⟩. ⟨hal-01352493⟩