Quantum parameter space in super Yang-Mills, II

TL;DR

This paper explores the quantum parameter space of super Yang-Mills theories with various gauge groups, revealing that quantum effects connect classically disconnected components through singularities and branch cuts, including novel strong coupling phenomena.

Contribution

It demonstrates that the quantum parameter space is connected for higher rank gauge groups, generalizing previous results and identifying new strong coupling singularities.

Findings

Quantum space is connected for U(4) and higher groups.

Classical disconnected components are linked via singularities or branch cuts.

New strong coupling singularities where glueballs become massless.

Abstract

In [1] (hep-th/0211069), the author has discussed the quantum parameter space of the N=1 super Yang-Mills theory with one adjoint Higgs field Phi, tree-level superpotential W_tree = m (Phi^2)/2 + g (Phi^3)/3$, and gauge group U(Nc). In particular, full details were worked out for U(2) and U(3). By discussing higher rank gauge groups like U(4), for which the classical parameter space has a large number of disconnected components, we show that the phenomena discussed in [1] are generic. It turns out that the quantum space is connected. The classical components are related in the quantum theory either through standard singularities with massless monopoles or by branch cuts without going through any singularity. The branching points associated with the branch cuts correspond to new strong coupling singularities, which are not associated with vanishing cycles in the geometry, and at which glueballs can become massless. The transitions discussed recently by Cachazo, Seiberg and Witten are special instances of those phenomena.