Field-Dependent Metrics and Higher-Form Symmetries in Duality-Invariant Theories of Non-Linear Electrodynamics
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913657632325632 |
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| author | Ferko, Christian Martin, Cian Luke |
| author_facet | Ferko, Christian Martin, Cian Luke |
| contents | We prove that a $4d$ theory of non-linear electrodynamics has equations of motion which are equivalent to those of the Maxwell theory in curved spacetime, but with the usual metric $g_{μν}$ replaced by a unit-determinant metric $h_{μν} ( F )$ which is a function of the field strength $F_{μν}$, if and only if the theory enjoys electric-magnetic duality invariance. Among duality-invariant models, the Modified Maxwell (ModMax) theory is special because the associated metric $h_{μν} ( F )$ produces identical equations of motion when it is coupled to the Maxwell theory via two different prescriptions which we describe. We use the field-dependent metric perspective to analyze the electric and magnetic $1$-form global symmetries in models of self-dual electrodynamics. This analysis suggests that any duality-invariant theory possesses a set of conserved currents $j^μ$ which are in one-to-one correspondence with $2$-forms that are harmonic with respect to the field-dependent metric $h_{μν} ( F )$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_17194 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Field-Dependent Metrics and Higher-Form Symmetries in Duality-Invariant Theories of Non-Linear Electrodynamics Ferko, Christian Martin, Cian Luke High Energy Physics - Theory Strongly Correlated Electrons High Energy Physics - Phenomenology Mathematical Physics We prove that a $4d$ theory of non-linear electrodynamics has equations of motion which are equivalent to those of the Maxwell theory in curved spacetime, but with the usual metric $g_{μν}$ replaced by a unit-determinant metric $h_{μν} ( F )$ which is a function of the field strength $F_{μν}$, if and only if the theory enjoys electric-magnetic duality invariance. Among duality-invariant models, the Modified Maxwell (ModMax) theory is special because the associated metric $h_{μν} ( F )$ produces identical equations of motion when it is coupled to the Maxwell theory via two different prescriptions which we describe. We use the field-dependent metric perspective to analyze the electric and magnetic $1$-form global symmetries in models of self-dual electrodynamics. This analysis suggests that any duality-invariant theory possesses a set of conserved currents $j^μ$ which are in one-to-one correspondence with $2$-forms that are harmonic with respect to the field-dependent metric $h_{μν} ( F )$. |
| title | Field-Dependent Metrics and Higher-Form Symmetries in Duality-Invariant Theories of Non-Linear Electrodynamics |
| topic | High Energy Physics - Theory Strongly Correlated Electrons High Energy Physics - Phenomenology Mathematical Physics |
| url | https://arxiv.org/abs/2406.17194 |