Abstract
We propose an effective field theory for branes with higher-form symmetry as a generalization of ordinary Landau theory, which is an extension of the previous work by Iqbal and McGreevy for one-dimensional objects to an effective theory for p-dimensional objects. In the case of a p-form symmetry, the fundamental field ψ[Cp] is a functional of p-dimensional closed brane Cp embedded in a spacetime. As a natural generalization of ordinary field theory, we call this theory the brane field theory. In order to construct an action that is invariant under higher-form transformation, we generalize the idea of area derivative for one-dimensional objects to higher-dimensional ones. Following this, we discuss various fundamental properties of the brane field based on the higher-form invariant action. It is shown that the classical solution exhibits the area law in the unbroken phase of U(1) p-form symmetry, while it indicates a constant behavior in the broken phase for the large volume limit of Cp. In the latter case, the low-energy effective theory is described by the p-form Maxwell theory. We also discuss brane-field theories with a discrete higher-form symmetry and show that the low-energy effective theory becomes a BF-type topological field theory, resulting in topological order. Finally, we present a concrete brane-field model that describes a superconductor from the point of view of higher-form symmetry.
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Acknowledgments
Y.H. would like to thank Ryo Yokokura for the useful discussions. The work of K.K. is supported by KIAS Individual Grants, Grant No. 090901. The work of Y.H. is supported by Japan Society for the Promotion of Science (JSPS) KAKENHI Grant Nos. 21H01084.
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Hidaka, Y., Kawana, K. Effective brane field theory with higher-form symmetry. J. High Energ. Phys. 2024, 16 (2024). https://doi.org/10.1007/JHEP01(2024)016
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DOI: https://doi.org/10.1007/JHEP01(2024)016