Advances in Theoretical and Mathematical Physics

Volume 21 (2017)

Number 7

Special Issue: Proceedings of the Strings 2016 Conference in Beijing

Guest Editors: J. Maldacena (Institute for Advanced Study), H. Ooguri (California Institute of Technology), H. Babak (Harvard University), S. Li (Tsinghua University), W. Song (Tsinghua University), and H. Lin (Tsinghua University)

On topological approach to local theory of surfaces in Calabi–Yau threefolds

Pages: 1679 – 1728

DOI: https://dx.doi.org/10.4310/ATMP.2017.v21.n7.a4

Authors

Sergei Gukov (Institute for Theoretical Physics, California Institute of Technology, Pasadena, Cal., U.S.A.; and Max-Planck-Institut für Mathematik, Bonn, Germany)

Chiu-Chu Melissa Liu (Department of Mathematics, Columbia University, New York, N.Y., U.S.A.)

Artan Sheshmani (Department of Mathematics, Aarhus University, Aarhus, Denmark; CMSA, Harvard University, Cambridge, Massachusetts, U.S.A.; and National Research University Higher School of Economics, Laboratory of Mirror Symmetry, Moscow, Russia)

Shing-Tung Yau (Department of Mathematics, Harvard University, Cambridge, Massachusetts, U.S.A.)

Abstract

We study the web of dualities relating various enumerative invariants, notably Gromov–Witten invariants and invariants that arise in topological gauge theory. In particular, we study Donaldson–Thomas gauge theory and its reductions to $D = 4$ and $D = 2$ which are relevant to the local theory of surfaces in Calabi–Yau threefolds.

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Published 19 March 2018