A one-to-one correspondence is established between anomalous boundary SETs and critical states of internal versus crystalline fermionic SPT phases, including explicit mappings of time-reversal and mirror anomaly indicators.
Two of the roots are protected by only time reversal or mirror symmetry, which can be detected by the above mentioned two anomaly indicators η1 and ηT or ηM
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Correspondence of boundary theories between internal and crystalline symmetry protected topological phases
A one-to-one correspondence is established between anomalous boundary SETs and critical states of internal versus crystalline fermionic SPT phases, including explicit mappings of time-reversal and mirror anomaly indicators.