Abstract
We show that three-dimensional trace anomalies lead to new universal anomalous transport effects on a conformally-flat spacetime with background scalar fields. In contrast to conventional anomalous transports in quantum chromodynamics (QCD) or quantum electrodynamics (QED), our current is independent of background gauge fields. Therefore, our anomalous transport survives even in the absence of vector-like external sources. By manipulating background fields, we suggest a setup to detect our anomalous transport. If one turns on scalar couplings in a finite interval and considers a conformal factor depending just on (conformal) time, we find anomalous transport localized at the interfaces of the interval flows perpendicularly to the interval. The magnitude of the currents is the same on the two interfaces but with opposite directions. Without the assumption on scalar couplings, and only assuming the conformal factor depending solely on (conformal) time as usually done in cosmology, one also finds the three-dimensional Hubble parameter naturally appears in our current.
Highlights
Quantum field theories (QFTs) often have anomalies in global symmetries, called ’t Hooft anomalies [1], which characterize QFTs
A remarkable example is the a theorem [2]. They coupled a theory to a background metric specified by a “dilaton.” Some terms of the dilaton effective action survive even after taking the flat limit, which were used to show the a theorem in four-dimensional QFTs defined on the Minkowski space
An important lesson one can learn from this example is that anomalies can have remnants even after turning off background fields introduced to diagnose anomalies
Summary
We show that three-dimensional trace anomalies lead to new universal anomalous transport effects on a conformally flat space-time with background scalar fields. In contrast to conventional anomalous transports in quantum chromodynamics or quantum electrodynamics, our current is independent of background gauge fields. Our anomalous transport survives even in the absence of vectorlike external sources. We suggest a setup to detect our anomalous transport. If one turns on scalar couplings in a finite interval and considers a conformal factor depending just on (conformal) time, we find anomalous transport localized at the interfaces of the interval flows perpendicularly to the interval. Without the assumption on scalar couplings, and only assuming the conformal factor depending solely on (conformal) time as usually done in cosmology, one finds the three-dimensional Hubble parameter naturally appears in our current
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