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| Format: | Preprint |
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2024
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| Online Access: | https://arxiv.org/abs/2410.18700 |
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| _version_ | 1866909371633500160 |
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| author | Maj, Antonina |
| author_facet | Maj, Antonina |
| contents | We consider four-dimensional non-Abelian gauge theory living on a complex projective space $\mathbb{CP}^2$ as a way of gaining insights into (3+1)-dimensional QCD. In particular, we use a complex parametrization of gauge fields on which gauge transformations act homogeneously. This allows us to factor out the gauge degrees of freedom from the volume element leading to a manifestly gauge-invariant measure for the gauge-orbit space (the space of all gauge potentials modulo gauge transformations). The terms appearing in the measure that are of particular interest are mass-like terms for the gauge-invariant modes of the gauge fields. Since these mass terms come with dimensional parameters they are significant in the context of dimensional transmutation. Moreover, the existence of local gauge-invariant mass terms on $\mathbb{CP}^2$ could be related to Schwinger-Dyson calculations of the soft gluon mass. Finally, we argue that there is a kinematic regime in which the theory can be approximated by a 4d Wess-Zumino-Witten (WZW) theory. This result can be used to draw similarities between the mechanism of confinement in four and (2+1) dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_18700 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A gauge-invariant measure for gauge fields on $\mathbb{CP}^2$ Maj, Antonina High Energy Physics - Theory We consider four-dimensional non-Abelian gauge theory living on a complex projective space $\mathbb{CP}^2$ as a way of gaining insights into (3+1)-dimensional QCD. In particular, we use a complex parametrization of gauge fields on which gauge transformations act homogeneously. This allows us to factor out the gauge degrees of freedom from the volume element leading to a manifestly gauge-invariant measure for the gauge-orbit space (the space of all gauge potentials modulo gauge transformations). The terms appearing in the measure that are of particular interest are mass-like terms for the gauge-invariant modes of the gauge fields. Since these mass terms come with dimensional parameters they are significant in the context of dimensional transmutation. Moreover, the existence of local gauge-invariant mass terms on $\mathbb{CP}^2$ could be related to Schwinger-Dyson calculations of the soft gluon mass. Finally, we argue that there is a kinematic regime in which the theory can be approximated by a 4d Wess-Zumino-Witten (WZW) theory. This result can be used to draw similarities between the mechanism of confinement in four and (2+1) dimensions. |
| title | A gauge-invariant measure for gauge fields on $\mathbb{CP}^2$ |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2410.18700 |