Abstract
Odd-dimensional quantum field theories (QFTs) can have nonzero trace anomalies if external fields are introduced and some ingredients needed to make Lorentz scalars with appropriate mass dimensions (or weights) are supplied. We have studied a three-dimensional QFT and explicitly computed the trace of the stress tensor using the holographic local renormalization group (RG). We have checked some properties of vector beta functions and the Wess-Zumino consistency condition, however, found the anomalies vanish on fixed points. We clarify what is responsible for the vanishing trace anomalies.
Highlights
Without a doubt, symmetry plays a central role in physics
We expected we could get nonzero trace anomalies even on conformal fixed points if we break the parity symmetry, but we have eventually showed it is not the case
We know that the trace of the stress tensor has a weight w = 3 and the non-local action Γ has w = 0
Summary
Symmetry plays a central role in physics. For example, spacetime symmetries impose various conservation laws, which govern classical physics almost completely. Analysis According to [12], the vector β functions must satisfy some properties such as (i) gradient property, (ii) compensated gauge invariance, (iii) orthogonality, (iv) Higgs-like relation, and (v) non-renormalization condition. These properties are confirmed to be satisfied in even-dimensions [8], one can see that they are satisfied in three spacetime dimensions: (i) the gradient property βa ∝ δSloc/δAa is manifested in the expression (37), (ii) the compensated gauge invariance follows trivially since the Virial current v vanishes, (iii) the orthogonality can be seen via an explicit computation thanks to the gauge invariance of.
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