Built on

J. Wang, X.-G. Wen, and S.-T. Yau, “Quantum Statistics and Spacetime Topology: Quantum Surgery Formulas,” Annals Phys
Original
1901
Earlier work this paper cites.
P.-S. Hsin and A. Turzillo, “Symmetry-Enriched Quantum Spin Liquids in ( 3 + 1 ) d (3+1)d ,” arXiv:1904.11550 [cond-mat.str-el]
Original
1904
Earlier work this paper cites.
E. Poppitz and T. A. Ryttov, “A possible phase for adjoint QCD,” arXiv:1904.11640 [hep-th]
Original
1904
Earlier work this paper cites.
Z. Wan, J. Wang, and Y. Zheng, “Quantum Yang-Mills 4d Theory and Time-Reversal Symmetric 5d Higher-Gauge TQFT: Anyonic-String/Brane Braiding Statistics to Topological Link Invariants,” arXiv:1904.00994 [hep-th]
Original
1904
Earlier work this paper cites.
C. Córdova, D. S. Freed, H. T. Lam, and N. Seiberg, “Anomalies in the Space of Coupling Constants and Their Dynamical Applications I,” arXiv:1905.09315 [hep-th]
Original
1905
Earlier work this paper cites.
C. Córdova, D. S. Freed, H. T. Lam, and N. Seiberg, “Anomalies in the Space of Coupling Constants and Their Dynamical Applications II,” arXiv:1905.13361 [hep-th]
Original
1905
Earlier work this paper cites.
R. Kobayashi, K. Ohmori, and Y. Tachikawa, “On gapped boundaries for SPT phases beyond group cohomology,” arXiv:1905.05391 [cond-mat.str-el]
Original
1905
Earlier work this paper cites.
J. Armas and A. Jain, “Viscoelastic hydrodynamics and holography,” arXiv:1908.01175 [hep-th]
Original
1908
Earlier work this paper cites.
L. V. Delacrétaz, D. M. Hofman, and G. Mathys, “Superfluids as Higher-form Anomalies,” arXiv:1908.06977 [hep-th]
Original
1908
Earlier work this paper cites.
C. Cordova and K. Ohmori, “Anomaly Constraints on Gapped Phases with Discrete Chiral Symmetry,” arXiv:1912.13069 [hep-th]
Original
1912
Earlier work this paper cites.
E. H. Lieb, T. Schultz, and D. Mattis, “Two soluble models of an antiferromagnetic chain,” Annals Phys
1961
Earlier work this paper cites.
J. Wess and B. Zumino, “Consequences of anomalous Ward identities,” Phys. Lett
1971
Earlier work this paper cites.
G. ’t Hooft, “Naturalness, chiral symmetry, and spontaneous chiral symmetry breaking,” NATO Sci. Ser. B
1980
Earlier work this paper cites.
S. R. Coleman and B. Grossman, “’t Hooft’s Consistency Condition as a Consequence of Analyticity and Unitarity,” Nucl. Phys
1982
Earlier work this paper cites.
A. N. Redlich, “Gauge Noninvariance and Parity Violation of Three-Dimensional Fermions,” Phys. Rev. Lett
1983
Earlier work this paper cites.
A. N. Redlich, “Parity Violation and Gauge Noninvariance of the Effective Gauge Field Action in Three-Dimensions,” Phys. Rev
1983
Earlier work this paper cites.
E. Witten, “Global Aspects of Current Algebra,” Nucl. Phys
1983
Earlier work this paper cites.
C. G. Callan, Jr. and J. A. Harvey, “Anomalies and Fermion Zero Modes on Strings and Domain Walls,” Nucl. Phys
1985
Earlier work this paper cites.
L. Alvarez-Gaume and P. H. Ginsparg, “The Structure of Gauge and Gravitational Anomalies,” Annals Phys
1985
Earlier work this paper cites.
L. Alvarez-Gaume, S. Della Pietra, and G. W. Moore, “Anomalies and Odd Dimensions,” Annals Phys
1985
Earlier work this paper cites.
J. J. van der Bij, R. D. Pisarski, and S. Rao, “Topological Mass Term for Gravity Induced by Matter,” Phys. Lett
1986
Earlier work this paper cites.
PhD thesis, Utrecht University, 1989
R. H. Dijkgraaf, A geometrical approach to two-dimensional Conformal Field Theory · 1989
Earlier work this paper cites.

Similar

B. Durhuus and T. Jonsson, “Classification and construction of unitary topological field theories in two-dimensions,” J. Math. Phys
1994
Cited alongside, same era.
S. Sawin, “Direct sum decompositions and indecomposable TQFTs,” J. Math. Phys
1995
Cited alongside, same era.
E. Witten, “Supersymmetric index in four-dimensional gauge theories,” Adv. Theor. Math. Phys
2002
Cited alongside, same era.
D. S. Freed and G. W. Moore, “Setting the quantum integrand of M-theory,” Commun. Math. Phys
2006
Cited alongside, same era.
M. Unsal, “Abelian duality, confinement, and chiral symmetry breaking in QCD(adj),” Phys. Rev. Lett
Original
2008
Cited alongside, same era.
M. Unsal, “Magnetic bion condensation: A New mechanism of confinement and mass gap in four dimensions,” Phys. Rev

Then

O. Aharony, F. Benini, P.-S. Hsin, and N. Seiberg, “Chern-Simons-matter dualities with S O SO and U S p USp gauge groups,” JHEP
Original
2017
Later among the works it cites.
C. Wang and M. Levin, “Anomaly indicators for time-reversal symmetric topological orders,” Phys. Rev. Lett
Original
2017
Later among the works it cites.
D. Gaiotto, A. Kapustin, Z. Komargodski, and N. Seiberg, “Theta, Time Reversal, and Temperature,” JHEP
Original
2017
Later among the works it cites.
C. Córdova, P.-S. Hsin, and N. Seiberg, “Time-Reversal Symmetry, Anomalies, and Dualities in (2+1) d d ,” SciPost Phys
Original
2018
Later among the works it cites.
D. Gaiotto, Z. Komargodski, and N. Seiberg, “Time-reversal breaking in QCD 4

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2019

Anomaly Obstructions to Symmetry Preserving Gapped Phases

Cordova, Clay, Ohmori, Kantaro

Understand

Anomalies are renormalization group invariants that constrain the dynamics of quantum field theories.

We show that certain anomalies for discrete global symmetries imply that the underlying theory either spontaneously breaks its generalized global symmetry or is gapless.
We identify an obstruction, formulated in terms of the anomaly inflow action, that must vanish if a symmetry preserving gapped phase, i.e.
a unitary topological quantum field theory, exits with the given anomaly.

Built on

J. Wang, X.-G. Wen, and S.-T. Yau, “Quantum Statistics and Spacetime Topology: Quantum Surgery Formulas,” Annals Phys
Original
1901
Earlier work this paper cites.
P.-S. Hsin and A. Turzillo, “Symmetry-Enriched Quantum Spin Liquids in ( 3 + 1 ) d (3+1)d ,” arXiv:1904.11550 [cond-mat.str-el]
Original
1904
Earlier work this paper cites.
E. Poppitz and T. A. Ryttov, “A possible phase for adjoint QCD,” arXiv:1904.11640 [hep-th]
Original
1904
Earlier work this paper cites.
Z. Wan, J. Wang, and Y. Zheng, “Quantum Yang-Mills 4d Theory and Time-Reversal Symmetric 5d Higher-Gauge TQFT: Anyonic-String/Brane Braiding Statistics to Topological Link Invariants,” arXiv:1904.00994 [hep-th]
Original
1904
Earlier work this paper cites.
C. Córdova, D. S. Freed, H. T. Lam, and N. Seiberg, “Anomalies in the Space of Coupling Constants and Their Dynamical Applications I,” arXiv:1905.09315 [hep-th]
Original
1905
Earlier work this paper cites.
C. Córdova, D. S. Freed, H. T. Lam, and N. Seiberg, “Anomalies in the Space of Coupling Constants and Their Dynamical Applications II,” arXiv:1905.13361 [hep-th]
Original
1905
Earlier work this paper cites.
R. Kobayashi, K. Ohmori, and Y. Tachikawa, “On gapped boundaries for SPT phases beyond group cohomology,” arXiv:1905.05391 [cond-mat.str-el]
Original
1905
Earlier work this paper cites.
J. Armas and A. Jain, “Viscoelastic hydrodynamics and holography,” arXiv:1908.01175 [hep-th]
Original
1908
Earlier work this paper cites.
L. V. Delacrétaz, D. M. Hofman, and G. Mathys, “Superfluids as Higher-form Anomalies,” arXiv:1908.06977 [hep-th]
Original
1908
Earlier work this paper cites.
C. Cordova and K. Ohmori, “Anomaly Constraints on Gapped Phases with Discrete Chiral Symmetry,” arXiv:1912.13069 [hep-th]
Original
1912
Earlier work this paper cites.
E. H. Lieb, T. Schultz, and D. Mattis, “Two soluble models of an antiferromagnetic chain,” Annals Phys
1961
Earlier work this paper cites.
J. Wess and B. Zumino, “Consequences of anomalous Ward identities,” Phys. Lett
1971
Earlier work this paper cites.
G. ’t Hooft, “Naturalness, chiral symmetry, and spontaneous chiral symmetry breaking,” NATO Sci. Ser. B
1980
Earlier work this paper cites.
S. R. Coleman and B. Grossman, “’t Hooft’s Consistency Condition as a Consequence of Analyticity and Unitarity,” Nucl. Phys
1982
Earlier work this paper cites.
A. N. Redlich, “Gauge Noninvariance and Parity Violation of Three-Dimensional Fermions,” Phys. Rev. Lett
1983
Earlier work this paper cites.
A. N. Redlich, “Parity Violation and Gauge Noninvariance of the Effective Gauge Field Action in Three-Dimensions,” Phys. Rev
1983
Earlier work this paper cites.
E. Witten, “Global Aspects of Current Algebra,” Nucl. Phys
1983
Earlier work this paper cites.
C. G. Callan, Jr. and J. A. Harvey, “Anomalies and Fermion Zero Modes on Strings and Domain Walls,” Nucl. Phys
1985
Earlier work this paper cites.
L. Alvarez-Gaume and P. H. Ginsparg, “The Structure of Gauge and Gravitational Anomalies,” Annals Phys
1985
Earlier work this paper cites.
L. Alvarez-Gaume, S. Della Pietra, and G. W. Moore, “Anomalies and Odd Dimensions,” Annals Phys
1985
Earlier work this paper cites.
J. J. van der Bij, R. D. Pisarski, and S. Rao, “Topological Mass Term for Gravity Induced by Matter,” Phys. Lett
1986
Earlier work this paper cites.
PhD thesis, Utrecht University, 1989
R. H. Dijkgraaf, A geometrical approach to two-dimensional Conformal Field Theory · 1989
Earlier work this paper cites.

Similar

B. Durhuus and T. Jonsson, “Classification and construction of unitary topological field theories in two-dimensions,” J. Math. Phys
1994
Cited alongside, same era.
S. Sawin, “Direct sum decompositions and indecomposable TQFTs,” J. Math. Phys
1995
Cited alongside, same era.
E. Witten, “Supersymmetric index in four-dimensional gauge theories,” Adv. Theor. Math. Phys
2002
Cited alongside, same era.
D. S. Freed and G. W. Moore, “Setting the quantum integrand of M-theory,” Commun. Math. Phys
2006
Cited alongside, same era.
M. Unsal, “Abelian duality, confinement, and chiral symmetry breaking in QCD(adj),” Phys. Rev. Lett
Original
2008
Cited alongside, same era.
M. Unsal, “Magnetic bion condensation: A New mechanism of confinement and mass gap in four dimensions,” Phys. Rev

Then

O. Aharony, F. Benini, P.-S. Hsin, and N. Seiberg, “Chern-Simons-matter dualities with S O SO and U S p USp gauge groups,” JHEP
Original
2017
Later among the works it cites.
C. Wang and M. Levin, “Anomaly indicators for time-reversal symmetric topological orders,” Phys. Rev. Lett
Original
2017
Later among the works it cites.
D. Gaiotto, A. Kapustin, Z. Komargodski, and N. Seiberg, “Theta, Time Reversal, and Temperature,” JHEP
Original
2017
Later among the works it cites.
C. Córdova, P.-S. Hsin, and N. Seiberg, “Time-Reversal Symmetry, Anomalies, and Dualities in (2+1) d d ,” SciPost Phys
Original
2018
Later among the works it cites.
D. Gaiotto, Z. Komargodski, and N. Seiberg, “Time-reversal breaking in QCD 4

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

Original

2009

Cited alongside, same era.

E. Poppitz, T. Schäfer, and M. Unsal, “Continuity, Deconfinement, and (Super) Yang-Mills Theory,” JHEP

Original

2012

Cited alongside, same era.

A. Kitaev, “On the classification of short-range entangled states,” Seminar at Simons Center for Geometry and Physics, 2013

2013

Cited alongside, same era.

L. Fidkowski, X. Chen, and A. Vishwanath, “Non-Abelian Topological Order on the Surface of a 3D Topological Superconductor from an Exactly Solved Model,” Phys. Rev

Original

2013

Cited alongside, same era.

M. Shifman, “Remarks on Adjoint QCD with k k Flavors, k ≥ 2 k\geq 2 ,” Mod. Phys. Lett

Original

2013

Cited alongside, same era.

J. Fuchs, C. Schweigert, and A. Valentino, “Bicategories for boundary conditions and for surface defects in 3-d TFT,” Commun. Math. Phys

Original

2013

Cited alongside, same era.

E. Poppitz, T. Schäfer, and M. Ünsal, “Universal mechanism of (semi-classical) deconfinement and theta-dependence for all simple groups,” JHEP

Original

2013

Cited alongside, same era.

Original

2018