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DOE OSTI · 1853641

A Metric on Directed Graphs and Markov Chains Based on Hitting Probabilities

Boyd, Zachary M.·Fraiman, Nicolas·Marzuola, Jeremy (ORCID:0000000286687143)·Mucha, Peter J.·Osting, Braxton (ORCID:0000000241239048)·Weare, Jonathan
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Boyd, Zachary M., Fraiman, Nicolas, Marzuola, Jeremy (ORCID:0000000286687143), Mucha, Peter J., Osting, Braxton (ORCID:0000000241239048), Weare, Jonathan. 2021-01-01. A Metric on Directed Graphs and Markov Chains Based on Hitting Probabilities. https://doi.org/10.1137/20m1348315

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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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