Recursive relations for a quiver gauge theory

TL;DR

This paper develops recursive relations for calculating scattering amplitudes in a specific two-gauge-group quiver theory, demonstrating improved efficiency and consistency with known results.

Contribution

It introduces a new recursive relation for quiver gauge theories with two gauge groups, enhancing computational efficiency and preserving permutation invariance.

Findings

Recursive relations verified for MHV, 6-point, and 7-point amplitudes.

Relations agree with known single gauge group amplitude results.

Proposed recursive method is more efficient than existing approaches.

Abstract

We study the recursive relations for a quiver gauge theory with the gauge group $SU(N_1)\times SU(N_2)$ with bifundamental fermions transforming as $(N_1,\bar{N_2})$. We work out the recursive relation for the amplitudes involving a pair of quark and antiquark and gluons of each gauge group. We realize directly in the recursive relations the invariance under the order preserving permutations of the gluons of the first and the second gauge group. We check the proposed relations for MHV, 6-point and 7-point amplitudes and find the agreements with the known results and the known relations with the single gauge group amplitudes. The proposed recursive relation is much more efficient in calculating the amplitudes than using the known relations with the amplitudes of the single gauge group.