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JOURNALS // Symmetry, Integrability and Geometry: Methods and Applications // Archive

SIGMA, 2024 Volume 20, 106, 27 pp. (Mi sigma2108)

Global Magni4icence, or: 4G Networks

Nikita Nekrasova, Nicolò Piazzalungab

a Simons Center for Geometry and Physics, Stony Brook University, Stony Brook, NY 11794-3636, USA
b New High Energy Theory Center, Rutgers University, USA

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.

Keywords: vertex, Calabi–Yau fourfold, Donaldson–Thomas, localization.

MSC: 14N35, 81T30, 81T60

Received: February 20, 2024; in final form November 15, 2024; Published online November 28, 2024

Language: English

DOI: 10.3842/SIGMA.2024.106


ArXiv: 2306.12995


© Steklov Math. Inst. of RAS, 2025