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We investigate the interactions of discrete zero-form and one-form globalsymmetries in (1+1)d theories. Focus is put on the interactions that thesymmetries can have on each other, which in this low dimension result in2-group symmetries or symmetry fractionalization. A large part of thediscussion will be to understand a major feature in (1+1)d: the multiplesectors into which a theory decomposes. We perform gauging of the one-formsymmetry, and remark on the effects this has on our theories, especially in thecase when there is a global 2-group symmetry. We also implement the spectralsequence to calculate anomalies for the 2-group theories and symmetryfractionalized theory in the bosonic and fermionic cases. Lastly, we discusstopological manipulations on the operators which implement the symmetries, anddraw insights on the (1+1)d effects of such manipulations by coupling to a bulk(2+1)d theory.

Symmetries and Anomalies of (1+1)d Theories: 2-groups and Symmetry Fractionalization