Abstract
We investigate gauge anomalies in the context of orbifold conformal field theories. Such anomalies manifest as failures of modular invariance in the constituents of the orbifold partition function. We review how this irregularity is classified by cohomology and how extending the orbifold group can remove it. Working with such extensions requires an understanding of the consistent ways in which extending groups can act on the twisted states of the original symmetry, which leads us to a discrete-torsion like choice that exists in orbifolds with trivially-acting subgroups. We review a general method for constructing such extensions and investigate its application to orbifolds. Through numerous explicit examples we test the conjecture that consistent extensions should be equivalent to (in general multiple copies of) orbifolds by non-anomalous subgroups.
Highlights
When calculating the torus partition function of an orbifold conformal field theory (CFT), one forms partial traces that are group-twisted versions of the parent theory partition function
As with T transformations, these phases can be absorbed into the definition of the partial traces relative to the topological defect lines (TDLs) picture until we find a relation of a partial trace to itself, which happens after four successive S transformations
In each example we examined, the ability to find such a resolution depended on the existence of nontrivial quantum symmetries given by elements of H1ðG; K Þ which encode the action of the extending group K on the Gtwisted states
Summary
When calculating the torus partition function of an orbifold conformal field theory (CFT), one forms partial traces that are group-twisted versions of the parent theory partition function. The only consistent symmetry available to us is the trivial one, and the only consistent orbifold we could have found was the trivial one (i.e., the parent theory) This example demonstrates the notion of using group extensions to “cure” orbifolds by anomalous actions. Because the extending group acts trivially on the parent theory (though in general nontrivially on the G-twisted states), this story naturally requires an understanding of decomposition, which is the study of noneffective group actions in field theories [4,5,6,7] Because of this similarity, we are preparing companion papers [8,9] to this one which explore similar material from the more mathematical viewpoint of decomposition
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