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arXiv · 2306.12995

Global magni$4$icence, or: 4G Networks

Nikita Nekrasov·Nicolo Piazzalunga
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Abstract

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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Nikita Nekrasov, Nicolo Piazzalunga. 2023-06-22. Global magni$4$icence, or: 4G Networks. https://doi.org/10.3842/sigma.2024.106

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