The Effective Prepotential of N=2 Supersymmetric SO(N_c) and Sp(N_c) Gauge Theories

TL;DR

This paper computes the exact effective prepotentials for N=2 supersymmetric SO(N_c) and Sp(N_c) gauge theories, extending previous SU(N_c) results, and explicitly evaluates instanton contributions.

Contribution

It introduces a method to derive prepotentials for SO and Sp gauge theories from unitary cases, including instanton effects, expanding the scope of exact solutions.

Findings

Prepotentials exhibit expected logarithmic singularities.

Explicit one- and two-instanton contributions are calculated.

Results extend known SU(N_c) solutions to SO and Sp groups.

Abstract

We calculate the effective prepotentials for N=2 supersymmetric SO(N_c) and Sp(N_c) gauge theories, with an arbitrary number of hypermultiplets in the defining representation, from restrictions of the prepotentials for suitable N=2 supersymmetric gauge theories with unitary gauge groups. (This extends previous work in which the prepotential for N=2 supersymmetric SU(N_c) gauge theories was evaluated from the exact solution constructed out of spectral curves.) The prepotentials have to all orders the logarithmic singularities of the one-loop perturbative corrections, as expected from non-renormalization theorems. We evaluate explicitly the contributions of one- and two-instanton processes.