Abstract
We consider the relation between mixed global gauge gravitational anomalies and boundary conformal field theory in WZW models for simple Lie groups. The discrete symmetries of consideration are the centers of the simple Lie groups. These mixed anomalies prevent gauging them i.e, taking the orbifold by the center. The absence of anomalies impose conditions on the levels of WZW models. Next, we study the conformal boundary conditions for the original theories. We consider the existence of a conformal boundary state invariant under the action of the center. This also gives conditions on the levels of WZW models. By considering the combined action of the center and charge conjugation on boundary states, we reproduce the condition obtained in the orbifold analysis.
Highlights
The study of SPT phases gives a natural motivation to consider the anomalies of discrete symmetries and global anomalies
For Bn the existence of an invariant boundary state gives the same condition for the absence of the mixed global anomalies
For Cn the existence of an invariant boundary state gives the same condition for the absence of the mixed global anomalies
Summary
We consider the mixed gauge gravitational anomalies in (1 + 1)-dimensional CFTs. See for example [12, 22] If we assume this SL(2, Z) large diffeomorphism invariance, partition functions Z(ht,hx) are related to each other by modular transformations according to the map of boundary conditions (ht, hx) → (hat hbx, hct hdx). This means Z(1,h) = SZ(h,1) and Z(hl,h) = T lSZ(h,1). The first equation means that the twisted sector partition function Z(1,h) is determined by symmetry action Tr(h e−2πImτH ei2πReτP ) and its modular S transformation.
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