Factorization of Seiberg-Witten Curves with Fundamental Matter

TL;DR

This paper provides an explicit construction of Seiberg-Witten curve factorizations for N=2 theories with fundamental matter, including new results on gauge symmetry breaking and conditions for factorization.

Contribution

It introduces a detailed method for factorizing Seiberg-Witten curves with fundamental flavors and explores gauge symmetry breaking effects and period integrality conditions.

Findings

Explicit factorization construction for N=2 theories with fundamental matter

New results on gauge symmetry breaking from U(Nc) to U(N1) x U(N2)

Integrality of periods is necessary and sufficient for factorization

Abstract

We present an explicit construction of the factorization of Seiberg-Witten curves for N=2 theory with fundamental flavors. We first rederive the exact results for the case of complete factorization, and subsequently derive new results for the case with breaking of gauge symmetry U(Nc) to U(N1)xU(N2). We also show that integrality of periods is necessary and sufficient for factorization in the case of general gauge symmetry breaking. Finally, we briefly comment on the relevance of these results for the structure of N=1 vacua.