Abstract
We argue that there is an obstruction to placing theories with ’t Hooft anomalies on manifolds with a boundary, unless the symmetry associated with the anomaly can be represented as a non-invariance under an Abelian transformation. For a two dimensional conformal field theory we further demonstrate that all anomalies except the usual trace anomaly are incompatible on a manifold with a boundary. Our findings extend a known result whereby, under mild assumptions, Lagrangian theories with chiral matter cannot be canonically quantized.
Highlights
Novel studies have tied anomalies to transport [7,8,9,10,11,12,13] leading to new experimental signatures of anomalies in condensed matter systems [14, 15] and possibly astrophysical settings [16, 17]
Kristan Jensen,a Evgeny Shaverinb and Amos Yaromb aDepartment of Physics and Astronomy, San Francisco State University, San Francisco, CA 94132, U.S.A. bDepartment of Physics, Technion, Haifa 32000, Israel E-mail: kristanj@sfsu.edu, evgeny@tx.technion.ac.il, ayarom@physics.technion.ac.il Abstract: We argue that there is an obstruction to placing theories with ’t Hooft anomalies on manifolds with a boundary, unless the symmetry associated with the anomaly can be represented as a non-invariance under an Abelian transformation
In this work we have argued that the Wess-Zumino consistency condition prohibits the existence of ’t Hooft anomalies on manifolds with boundary at least when the anomalies are not of the form given in (2.55)
Summary
A classical symmetry is a transformation of the dynamical fields under which the action remains invariant. In quantum field theory a symmetry manifests itself as an invariance of the generating function W [A] under a transformation the external sources, for instance δvW [A] = W [A + δvA] − W [A] = 0 ,. Non trivial solutions to (2.6) exist in even dimensional spacetimes They can be obtained by converting (2.6) to a cohomological problem. In order to avoid setting vG = d (vGb) + dG (which implies a trivial solution to the Wess Zumino consistency conditions, δvW = dG ) we must first look for a solution of the form (2.14), and set d(vGb) = Q. We conclude that the Wess-Zumino consistency condition cannot be satisfied for theories with non-Abelian ’t Hooft anomalies on manifolds with boundaries. In the remainder of this section we will study the ramifications of this result in two, four, and higher dimensions
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