Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 20 (2024), 106, 27 pages      arXiv:2306.12995      https://doi.org/10.3842/SIGMA.2024.106

Global Magni4icence, or: 4G Networks

Nikita Nekrasov a and Nicolò Piazzalunga b
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

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

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.

Key words: vertex; Calabi-Yau fourfold; Donaldson-Thomas; localization.

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