Constraints on the BPS Spectrum of N = 2, D = 4 Theories with A-D-E Flavor Symmetry

TL;DR

This paper investigates the BPS spectrum in N=2, D=4 Super Yang-Mills theories with ADE flavor symmetry, revealing how junctions and lattice relations determine the spectrum and flavor representations.

Contribution

It establishes the connection between junction self-intersection bounds and the emergence of large flavor representations in ADE symmetric theories.

Findings

BPS spectrum for SU(2) with N_f <= 4 is characterized by junctions with bounded self-intersection.

Large flavor representations naturally appear for D_{n>=5} and E_n symmetries.

Decoupling to smaller symmetries is consistent with the presence of these large representations.

Abstract

BPS states of N=2, D=4 Super Yang-Mills theories with ADE flavor symmetry arise as junctions joining a D3-brane to a set of 7-branes defining the enhanced flavor algebra. We show that the familiar BPS spectrum of SU(2) theories with N_f <= 4 is simply given by the set of junctions whose self-intersection is bounded below as required by supersymmetry. This constraint, together with the relations between junction and weight lattices, is used to establish the appearance of arbitrarily large flavor representations for the case of D_{n>=5} and E_n symmetries. Such representations are required by consistency with decoupling down to smaller flavor symmetries.