References

[1]
Y. Tachikawa, Lecture on Anomalies and Topological Phases, (2019), https://member.ipmu.jp/yuji.tachikawa/lectures/2019-top-anom/.
[2]
C. Córdova, Symmetries and Anomalies, (2020), https://indico.cern.ch/event/857396/timetable/.
[3]
K. Ohmori, Topological Phases and Anomalies, (2020), https://sites.google.com/view/qftandgeometrysummerschool/home?authuser=0.
[4]
E. Witten, Three lectures on topological phases of matter, Riv. Nuovo Cim. 39, 313 (2016), https://arxiv.org/abs/1510.07698.
[5]
E. Witten, Fermion Path Integrals And Topological Phases, Rev. Mod. Phys. 88, 035001 (2016), https://arxiv.org/abs/1508.04715.
[6]
D. Gaiotto, A. Kapustin, Z. Komargodski, and N. Seiberg, Theta, Time Reversal, and Temperature, JHEP 05, 091 (2017), https://arxiv.org/abs/1703.00501.
[7]
C. Córdova and K. Ohmori, Anomaly Obstructions to Symmetry Preserving Gapped Phases, (2019), https://arxiv.org/abs/1910.04962.
[8]
S. Weinberg, The Quantum theory of fields. Vol. 1: Foundations (Cambridge University Press, 2005).
[9]
C. Córdova, D. S. Freed, H. T. Lam, and N. Seiberg, Anomalies in the Space of Coupling Constants and Their Dynamical Applications I, SciPost Phys. 8, 001 (2020), https://arxiv.org/abs/1905.09315.
[10]
X. Chen, Z.-C. Gu, Z.-X. Liu, and X.-G. Wen, Symmetry protected topological orders and the group cohomology of their symmetry group, Phys. Rev. B 87, 155114 (2013), https://arxiv.org/abs/1106.4772.
[11]
C. G. Callan Jr. and J. A. Harvey, Anomalies and Fermion Zero Modes on Strings and Domain Walls, Nucl. Phys. B 250, 427 (1985).
[12]
I. Affleck, T. Kennedy, E. H. Lieb, and H. Tasaki, Rigorous Results on Valence Bond Ground States in Antiferromagnets, Phys. Rev. Lett. 59, 799 (1987).
[13]
A. Prakash, J. Wang, and T.-C. Wei, Unwinding Short-Range Entanglement, Phys. Rev. B 98, 125108 (2018), https://arxiv.org/abs/1804.11236.
[14]
E. Witten, Why Does Quantum Field Theory In Curved Spacetime Make Sense? And What Happens To The Algebra of Observables In The Thermodynamic Limit?, (2021), https://arxiv.org/abs/2112.11614.
[15]
Z. Komargodski, K. Ohmori, K. Roumpedakis, and S. Seifnashri, Symmetries and strings of adjoint QCD\(_{2}\), JHEP 03, 103 (2021), https://arxiv.org/abs/2008.07567.
[16]
S. Hellerman, A. Henriques, T. Pantev, E. Sharpe, and M. Ando, Cluster decomposition, T-duality, and gerby CFT’s, Adv. Theor. Math. Phys. 11, 751 (2007), https://arxiv.org/abs/hep-th/0606034.
[17]
J. Polchinski, String theory. Vol. 1: An introduction to the bosonic string (Cambridge University Press, 2007).
[18]
R. Thorngren and Y. Wang, Anomalous symmetries end at the boundary, JHEP 09, 017 (2021), https://arxiv.org/abs/2012.15861.
[19]
S. Hellerman, D. Orlando, and M. Watanabe, Quantum Information Theory of the Gravitational Anomaly, (2021), https://arxiv.org/abs/2101.03320.
[20]
E. Witten, The ”Parity” Anomaly On An Unorientable Manifold, Phys. Rev. B 94, 195150 (2016), https://arxiv.org/abs/1605.02391.
[21]
J. Wang, X.-G. Wen, and E. Witten, Symmetric Gapped Interfaces of SPT and SET States: Systematic Constructions, Phys. Rev. X 8, 031048 (2018), https://arxiv.org/abs/1705.06728.