Global Magni4icence, or: 4G Networks

The global magnificent four theory is the homological version of a maximally supersymmetric (8 + 1)-dimensional gauge theory on a Calabi–Yau fourfold fibered over a circle. In the case of a toric fourfold we conjecture the formula for its twisted Witten index. String-theoretically we count the BPS states of a system of D0-D2-D4-D6-D8-branes on the Calabi–Yau fourfold in the presence of a large Neveu–Schwarz B-field. Mathematically, we develop the equivariant K-theoretic DT4 theory, by constructing the four-valent vertex with generic plane partition asymptotics. Physically, the vertex is a supersymmetric localization of a non-commutative gauge theory in 8 + 1 dimensions.