Computation of the Central Charge for the Leading Order of the N=2 Super-Yang-Mills Effective Action

TL;DR

This paper directly computes the central charge in N=2 Super-Yang-Mills theory at leading order, crucial for understanding BPS state masses, using the same holomorphic function as in the low energy effective action.

Contribution

It provides a direct calculation of the central charge for the leading order effective action in N=2 Super-Yang-Mills with gauge group SU(2).

Findings

Explicit expression for the central charge at leading order.

Connection between the central charge and the holomorphic function F.

Clarification of the role of the effective action in BPS spectrum analysis.

Abstract

The central charge in the N=2 Super-Yang-Mills theory plays an essential role in the work of Seiberg and Witten as it gives the mass spectrum of the BPS states of the quantum theory. Our aim in this note is to present a direct computation of this central charge for the leading order (in a momentum expansion) of the effective action. We will consider the N=2 Super-Yang-Mills theory with gauge group SU(2). The leading order of the effective action is given by the same holomorphic function F appearing in the low energy U(1) effective action.