Magnetic monopoles as gauge particles?

A euclidean lattice construction of supersymmetric Yang-Mills theories with sixteen supercharges

“…The vacuum expectation values of the bosonic link variables at this point in moduli space are interpreted as the inverse lengths of the corresponding links of the spacetime lattice, and the continuum limit is taken by moving out to infinity in moduli space. 3 Expanding about different points in moduli space can leave intact different symmetries, and correspond to different spacetime lattice structures. For example, if we were to choose the point where the z m and z m variables were equal and proportional to the identity matrix for those with r a = δ ai for i = 1, .…”

“…The action possess a global SO(3) × SO (7) symmetry, where SO(3) is the euclidean counterpart of the Lorentz symmetry and SO (7) is the R-symmetry of the theory. Under this symmetry the gauge bosons transform as (3,1), the scalars as (1, 7), and the fermions as (1, 8) ⊕ (1, 8). The action has a form form similar to that in eq.…”

“…[39] in order to try to shed light on the fascinating dualities present in N = 4 SYM theory in four [3] and three [40 -42] dimensions.…”

Mirror Symmetry, Hitchin's Equations, and Langlands Duality

“…Moreover, N = 4 supersymmetric Yang-Mills theory, originally constructed in Brink et al (1977), is a natural place to start, as it has the maximal possible supersymmetry, and has the celebrated duality whose origins go back to the early work of Montonen & Olive (1977). It indeed turns out that geometric Langlands has a natural origin in a twisted version of N = 4 super Yang-Mills theory in four dimensions.…”

The action of N = 4 Super Yang-Mills from a chiral primary operator

“…In the case of the twist proposed by Vafa and Witten [10] the SU(4) is splitted as SU(2) F × SU(2) I , so that the twisted global symmetry group turns out to be SU (2) (2) F is a residual internal symmetry group. The fields of the N = 4 multiplet are given by (A µ ,λ α u ,λ u α , Φ uv ), where (u, v = 1, .., 4) are indices of the fundamental representation of SU (4), and the six real scalar fields of the model are collected into the antisymmetric and selfconjugate tensor Φ uv . Under the twisted group, these fields decompose as…”