DOE OSTI · 1976765
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Osher, Stanley, Wang, Bao, Yin, Penghang, Luo, Xiyang, Barekat, Farzin, Pham, Minh, Lin, Alex. 2022-08-12. Laplacian smoothing gradient descent. https://doi.org/10.1007/s40687-022-00351-1
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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.