( − 1 ) -form symmetries and anomaly shifting from symmetry topological field theory

We investigate ( <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mo>−</a:mo> <a:mn>1</a:mn> </a:math> )-form symmetries using the framework of symmetry topological field theories. Previous studies of ( <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mo>−</c:mo> <c:mn>1</c:mn> </c:math> )-form symmetries have primarily focused in SymTFTs with topological point operators. Here we examine SymTFTs devoid of point operators, constructed to realize zero-form symmetries of some physical theory. In this context we identify codimension-one defects within the bulk of SymTFT constructed via higher gauging, which can be interpreted as the generators of ( <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mo>−</e:mo> <e:mn>1</e:mn> </e:math> )-form symmetry of the absolute theory. In addition, we present examples where ( <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mo>−</g:mo> <g:mn>1</g:mn> </g:math> )-form symmetries exhibit the novel ability to shift the ’t Hooft anomalies of the theory.