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2013

Higher symmetry and gapped phases of gauge theories

Kapustin, Anton, Thorngren, Ryan

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We study topological field theory describing gapped phases of gauge theories where the gauge symmetry is partially Higgsed and partially confined.

The TQFT can be formulated both in the continuum and on the lattice and generalizes Dijkgraaf-Witten theory by replacing a finite group by a finite 2-group.
The basic field in this TQFT is a 2-connection on a principal 2-bundle.
We classify topological actions for such theories as well as loop and surface observables.

Higher symmetry and gapped phases of gauge theories · Around

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Similar

E. Witten, “Quantum Field Theory and the Jones Polynomial,” Commun. Math. Phys. 121
1989
Cited alongside, same era.
R. Dijkgraaf and E. Witten, “Topological Gauge Theories and Group Cohomology,” Commun. Math. Phys. 129
1990
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F. Quinn, “Lectures on axiomatic topological quantum field theory,” in: Geometry and Quantum Field Theory, Park City, UT, 1991,
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J. Polchinski, “String theory. Vol. 2: Superstring theory and beyond,” Cambridge, UK: Univ. Pr. (1998) 531 p
1998
Cited alongside, same era.
S. Gukov and A. Kapustin, “Topological Quantum Field Theory, Nonlocal Operators, and Gapped Phases of Gauge Theories,” arXiv:1307.4793 [hep-th]
Original
Cited in the paper.
A. Kapustin and R. Thorngren, “Topological Field Theory on a Lattice, Discrete Theta-Angles and Confinement,” arXiv:1308.2926 [hep-th]
Original
Cited in the paper.
R. Thorngren, “Electric-Magnetic Duality of Topological Gauge Theories from Compactification,” arXiv:1309.1489 [hep-th]
Original
Cited in the paper.
D. S. Freed, M. J. Hopkins, J. Lurie and C. Teleman, “Topological Quantum Field Theories from Compact Lie Groups,” arXiv:0905.0731 [math.AT]
Original
Cited in the paper.
L. -Y. Hung and X. -G. Wen, “Quantized topological terms in weakly coupled gauge theories and their connection to symmetry protected topological phases,” arXiv:1211.2767 [cond-mat.str-el]
Original
Cited in the paper.
K. Walker and Z. Wang, “(3+1)-TQFTs and Topological Insulators,” arXiv:1104.2632 [cond-mat.str-el]
Original
Cited in the paper.
J. C. Baez, A. D. Lauda, “Higher-Dimensional Algebra V: 2-groups,” arXiv:math/0307200 [math.QA]
Cited in the paper.
J. Baez and U. Schreiber, “Higher gauge theory: 2-connections on 2-bundles,” hep-th/0412325
Cited in the paper.

Then

A. Hatcher, “Algebraic Topology,” Cambridge University Press, 2001
2001
Later among the works it cites.
M. Levin and Z. -C. Gu, “Braiding statistics approach to symmetry-protected topological phases,” Phys. Rev. B 86
Original
2012
Later among the works it cites.
X. Chen, Z. -C. Gu, Z. -X. Liu and X. -G. Wen, “Symmetry protected topological orders and the cohomology class of their symmetry group,” Phys. Rev. B 87
Original
2013
Closest in time.
C. W. von Keyserlingk, F. J. Burnell and S. H. Simon, “Three-dimensional topological lattice models with surface anyons,” Phys. Rev. B 87
Original
2013
Closest in time.

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