Two loop Kahler potential in beta-deformed N=4 SYM theory

TL;DR

This paper computes the two-loop corrections to the Kahler potential in a beta-deformed N=4 SYM theory, revealing non-trivial quantum effects due to reduced supersymmetry.

Contribution

It provides the first explicit calculation of two-loop Kahler potential corrections in a beta-deformed N=4 SYM, extending understanding of quantum effects in superconformal theories.

Findings

Two-loop Kahler potential depends on mass matrix diagonalization.

Explicit two-loop Kahler potential computed for SU(3) gauge group.

Results are presented in a superconformal form.

Abstract

In N=2 superconformal field theories the Kahler potential is known to be tree level exact. The beta-deformation of N=4 SU(N) SYM reduces the amount of supersymmetry to N=1, allowing for non-trivial, superconformal loop corrections to the Kahler potential. We analyse the two-loop corrections on the Coulomb branch for a complex deformation. For an arbitrary chiral field in the Cartan subalgebra we reduce the problem of computing the two-loop Kahler potential to that of diagonalising the mass matrix, we then present the result in a manifestly superconformal form. The mass matrix diagonalisation is performed for the case of the chiral background that induces the breaking pattern SU(N) -> SU(N-2)*U(1)^2. Then, for the gauge group SU(3), the Kahler potential is explicitly computed to the two-loop order.