Citation

BibTex format

@article{Duff:2020:1751-8121/ab956d,
author = {Duff, MJ},
doi = {1751-8121/ab956d},
journal = {Journal of Physics A: Mathematical and Theoretical},
title = {Weyl, Pontryagin, Euler, Eguchi and Freund},
url = {http://dx.doi.org/10.1088/1751-8121/ab956d},
volume = {53},
year = {2020}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - In a September 1976 PRL Eguchi and Freund considered two topological invariants: the Pontryagin number $P\sim \int {\mathrm{d}}^{4}x\sqrt{g}{R}^{{\ast}}R$ and the Euler number $\chi \sim \int {\mathrm{d}}^{4}x\sqrt{g}{R}^{{\ast}}{R}^{{\ast}}$ and posed the question: to what anomalies do they contribute? They found that P appears in the integrated divergence of the axial fermion number current, thus providing a novel topological interpretation of the anomaly found by Kimura in 1969 and Delbourgo and Salam in 1972. However, they found no analogous role for χ. This provoked my interest and, drawing on my April 1976 paper with Deser and Isham on gravitational Weyl anomalies, I was able to show that for conformal field theories the trace of the stress tensor depends on just two constants: ${g}^{\mu \nu }\langle {T}_{\mu \nu }\rangle =\frac{1}{{\left(4\pi \right)}^{2}}\left(cF-aG\right)$ where F is the square of the Weyl tensor and $\int {\mathrm{d}}^{4}x\sqrt{g}G/{\left(4\pi \right)}^{2}$ is the Euler number. For free CFTs with N s massless fields of spin s $720c=6{N}_{0}+18{N}_{1/2}+72{N}_{1}720a=2{N}_{0}+11{N}_{1/2}+124{N}_{1}$.
AU  - Duff,MJ
DO  - 1751-8121/ab956d
PY  - 2020///
SN  - 1751-8113
TI  - Weyl, Pontryagin, Euler, Eguchi and Freund
T2  - Journal of Physics A: Mathematical and Theoretical
UR  - http://dx.doi.org/10.1088/1751-8121/ab956d
UR  - http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000553710600001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
VL  - 53
ER  -
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