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DOE OSTI · 1891792

On arbitrarily regular conforming virtual element methods for elliptic partial differential equations

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Manzini, Gianmarco, Antonietti, P. F., Scacchi, S., Verani, M.. 2022-10-06. On arbitrarily regular conforming virtual element methods for elliptic partial differential equations. https://www.osti.gov/biblio/1891792

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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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