Kavli Affiliate: Austin Joyce
| First 5 Authors: Kurt Hinterbichler, Diego M. Hofman, Austin Joyce, Grégoire Mathys,
| Summary:
We study effective field theories (EFTs) enjoying (maximal) biform
symmetries. These are defined by the presence of a conserved (electric) current
that has the symmetries of a Young tableau with two columns of equal length.
When these theories also have a topological (magnetic) biform current, its
conservation law is anomalous. We go on to show that this mixed anomaly
uniquely fixes the two-point function between the electric and magnetic
currents. We then perform a K"all’en-Lehmann spectral decomposition of the
current-current correlator, proving that there is a massless mode in the
spectrum, whose masslessness is protected by the anomaly. Furthermore, the
anomaly gives rise to a universal form of the EFT whose most relevant term,
which resembles the linear Einstein action, dominates the infrared physics. As
applications of this general formalism, we study the theories of a Galileon
superfluid and linearized gravity. Thus, one can view the masslessness of the
graviton as being protected by the anomalous biform symmetries. The associated
EFT provides an organizing principle for gravity at low energies in terms of
physical symmetries, and allows interactions consistent with linearized
diffeomorphism invariance. These theories are not ultraviolet-complete, the
relevant symmetries can be viewed as emergent, nor do they include the
nonlinearities necessary to make them fully diffeomorphism invariant, so there
is no contradiction with the expectation that quantum gravity cannot have any
global symmetries.
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