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Communications in Mathematical Physics

, Volume 372, Issue 2, pp 573–597 | Cite as

Magnificent Four with Colors

  • Nikita Nekrasov
  • Nicolò PiazzalungaEmail author
Article

Abstract

We study the rank N magnificent four theory, which is the supersymmetric localization of U(N) super-Yang–Mills theory with matter (a super-group U(N|N) gauge theory) on a Calabi–Yau fourfold. Our theory contains the higher rank Donaldson–Thomas theory of threefolds. We conjecture an explicit formula for the partition function \({\mathcal {Z}}\), and report on the performed checks. The partition function \({\mathcal {Z}}\) has a free field representation. Surprisingly, it depends on the Coulomb and mass parameters in a simple way. We also clarify the definition of the instanton measure.

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Notes

Acknowledgements

NN thanks A. Okounkov for discussions, and MSRI (Berkeley), Department of Mathematics (UC Berkeley), IHES (Bures-sur-Yvette), and Skoltech (Moscow) for hospitality during the preparation of this work and for opportunity to present its preliminary results there. Research of NN is partially supported by Laboratory of Mirror Symmetry NRU HSE, RF Government grant, ag. N. 14.641.31.0001. NP thanks A. Grassi, A. Waldron and the participants of the workshops at ICTP Trieste (July 2018) and GGI Florence (April 2018), where this work was presented, for stimulating discussions. The research of NP was supported in part by Istituto Nazionale di Alta Matematica “Francesco Severi” (INdAM) and by Perimeter Institute for Theoretical Physics. (Research at Perimeter Institute is supported by the Government of Canada through the Department of Innovation, Science and Economic Development and by the Province of Ontario through the Ministry of Research and Innovation.)

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Simons Center for Geometry and PhysicsStony Brook UniversityStony BrookUSA

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