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Babak Haghighat

Associate Professor, Yau Mathematical Sciences Center, Tsinghua University

Basic Information

Email
babakhaghighat (at) tsinghua.edu.cn
Office
Shuangqing Complex Building B619

Research Areas

String theory, topological strings, supersymmetric gauge theory, M5/M-string systems, duality defects, SymTFT, and low-dimensional topological field theory.

Education

  • 2006/11-2009/10, Ph.D. in Mathematical Physics, University of Bonn.
  • 2001/10-2006/10, B.Sc. and M.Sc. in Physics, University of Bonn.

Employment

  • 2021/08-present, Associate Professor, Tsinghua University.
  • 2016/10-2021/08, Assistant Professor, Tsinghua University.
  • 2011/09-2016/09, Postdoctoral Fellow, Physics/Mathematics, Harvard University.
  • 2010/09-2011/08, Postdoctoral Fellow, Theoretical Physics, Utrecht University.
  • 2009/11-2010/08, Research Fellow, University of Bonn.

Research Summary

Babak Haghighat studies string theory and supersymmetric quantum field theory through the geometry and topology of compactification, defects, and conformal blocks. In recent work, KZ and irregular KZ connections, Rozansky-Witten foams, Vafa-Witten partition functions, SymTFT, and parafermionic defects appear as different manifestations of the same organizing principle: higher-dimensional supersymmetric theories can produce rich low-dimensional algebraic and topological structures. This continues his earlier work on topological strings, M-strings, and 6d SCFTs, while shifting the emphasis toward non-invertible defects, modularity, and representation-theoretic control of quantum field theory.

Representative Publications

  • B. Haghighat, J. Manschot, S. Vandoren, “A 5d/2d/4d correspondence,” JHEP 03 (2013) 157.
  • C. Cordova, S. Espahbodi, B. Haghighat, A. Rastogi, C. Vafa, “Tangles, Generalized Reidemeister Moves, and Three-Dimensional Mirror Symmetry,” JHEP 05 (2014) 014.
  • B. Haghighat, A. Iqbal, C. Kozcaz, G. Lockhart, C. Vafa, “M-Strings,” Commun. Math. Phys. 334 (2015) 779.
  • M. Alim, B. Haghighat, M. Hecht, A. Klemm, M. Rauch, T. Wotschke, “Wall-crossing holomorphic anomaly and mock modularity of multiple M5-branes,” Commun. Math. Phys. (2015).
  • X. Gu, B. Haghighat, Y. Liu, “Ising-like and Fibonacci anyons from KZ-equations,” JHEP 09 (2022) 015.
  • J. Chen, W. Cui, B. Haghighat, Y.-N. Wang, “SymTFTs and Duality Defects from 6d SCFTs on 4-manifolds,” JHEP 11 (2023) 208.
  • W. Cui, B. Haghighat, L. Ruggeri, “Non-invertible surface defects in 2+1d QFTs from half spacetime gauging,” JHEP 11 (2024) 159.
  • S. Gukov, B. Haghighat, N. Reshetikhin, “Foams and KZ-equations in Rozansky-Witten theories,” Nucl. Phys. B 1014 (2025) 116856, arXiv:2407.19757.

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