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DOE OSTI · 2580018

Generalizing Lloyd’s Algorithm for Graph Clustering

Zaman, Tareq·Nytko, Nicolas·Taghibakhshi, Ali·MacLachlan, Scott (ORCID:0000000263640684)·Olson, Luke (ORCID:0000000252836104)·West, Matthew
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Zaman, Tareq, Nytko, Nicolas, Taghibakhshi, Ali, MacLachlan, Scott (ORCID:0000000263640684), Olson, Luke (ORCID:0000000252836104), West, Matthew. 2024-09-03. Generalizing Lloyd’s Algorithm for Graph Clustering. https://doi.org/10.1137/23m1556800

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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.

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