Modified Abelian Gauge Theories

Abstract

The topological properties of field configurations in gauge theory contain important data about the (generalized) global symmetries of the theory as well as potential inconsistencies in the form of gauge anomalies. In this work we modify the topological classes of Abelian $p$-form fields, generating new global variants of gauge theories. These modifications implement constraints directly on the classifying space of the gauge field and its cohomology classes via homotopy fiber construction. This general approach allows us to investigate the universal effects of the constraints on the conserved global charges encoded in gauge characteristic classes. We further demonstrate that this procedure generically leads to new topological sectors introducing additional global charges and anomalies in the modified gauge theories.

Figures (30)

• Figure 1: Illustration of classifying maps $f$ from $X = S^1$ and $X = T^2$ to the classifying space of a periodic scalar field, $K(\mathbb{Z},1) \simeq S^1$.
• Figure 2: Illustration of the homotopy fiber construction of the 'times $n$' constraint for a periodic scalar field (for $X = T^2$ and $\alpha$ a double cover). Here, $f^{\ast}(v_1) = (\textcolor{red}{a}, \textcolor{blue}{b}) \in H^1(T^2;\mathbb{Z})$ denotes the pull-back of the fundamental class of the circle, $v_1$, with respect to $f$.
• Figure 3: Illustration of the homotopy fiber construction of the 'mod $n$' constraint for a periodic scalar field (for $X = T^2$ and $\alpha$ the non-trivial element in $H^1(S^1;\mathbb{Z}_2)$, i.e., $n=2$).
• Figure 4: Illustration of $Q$ in 'times $n$' constraint as $\mathbb{Z}$ fibered over $S^1$
• Figure 5: $E^{p,q}_2$ and $E^{p,q}_{\infty}$ page of $Q$ implementing $n c_1 = 0$.