ON THE GAUGE INVARIANCE OF WESS-ZUMINO-WITTEN EFFECTIVE ACTION

ZHOU Guang-Zhao; GUO Han-Ying; WU Ke; SONG Xing-Chang

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《中国物理C》（英文）编辑部

2024年10月30日

Chinese Physics C> 1984, Vol. 8> Issue(2) : 252-256

ON THE GAUGE INVARIANCE OF WESS-ZUMINO-WITTEN EFFECTIVE ACTION

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Abstract：
It is shown that in order to introduce the gauge invariant Wess-Zumino-Witten effective action a global anomalyfree condition should be satisfied by the gauged subgroup of SU(3)_L×SU(3)_R. The condition requires that the left handed and the right handed Chern-Simons 5-forms with respect to the gauge group be equal to each other and it turns out in the local sense to be the usual perturbative anomaly-free condition. It is also constructed a gauge invariant effective action under the anomaly-free condition by means of a systematic method rather than the trial and error Noether method. In the non-abelian case, the gauge invariant effective action presented here contains less terms than the one obtained by Witten. The case of pure gauge is discussed in the present note as well.
References

[1] E. WTitten "Global Aspects of Current Algebra", Princeton Preprint (1983).[2] J. Wess and B. Zumino, Phys. Lett., 37B(1971),95.

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ZHOU Guang-Zhao, GUO Han-Ying, WU Ke and SONG Xing-Chang. ON THE GAUGE INVARIANCE OF WESS-ZUMINO-WITTEN EFFECTIVE ACTION[J]. Chinese Physics C, 1984, 8(2): 252-256.

ZHOU Guang-Zhao, GUO Han-Ying, WU Ke and SONG Xing-Chang. ON THE GAUGE INVARIANCE OF WESS-ZUMINO-WITTEN EFFECTIVE ACTION[J]. Chinese Physics C, 1984, 8(2): 252-256. shu

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Received: 1900-01-01
Revised: 1900-01-01

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沈阳化工大学材料科学与工程学院沈阳 110142

ON THE GAUGE INVARIANCE OF WESS-ZUMINO-WITTEN EFFECTIVE ACTION

Corresponding author: ZHOU Guang-Zhao,

Received Date: 1900-01-01
Accepted Date: 1900-01-01
Available Online: 1984-04-05

Abstract: It is shown that in order to introduce the gauge invariant Wess-Zumino-Witten effective action a global anomalyfree condition should be satisfied by the gauged subgroup of SU(3)_L×SU(3)_R. The condition requires that the left handed and the right handed Chern-Simons 5-forms with respect to the gauge group be equal to each other and it turns out in the local sense to be the usual perturbative anomaly-free condition. It is also constructed a gauge invariant effective action under the anomaly-free condition by means of a systematic method rather than the trial and error Noether method. In the non-abelian case, the gauge invariant effective action presented here contains less terms than the one obtained by Witten. The case of pure gauge is discussed in the present note as well.