Analytic framework for self-dual criticality in $\mathbb{Z}_k$ gauge theory with matter
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866914866288132096 |
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| author | Shi, Zhengyan Darius Chatterjee, Arkya |
| author_facet | Shi, Zhengyan Darius Chatterjee, Arkya |
| contents | We study the putative multicritical point in 2+1D $\mathbb{Z}_k$ gauge theory where the Higgs and confinement transitions meet. The presence of an $e$-$m$ duality symmetry at this critical point forces anyons with nontrivial braiding to close their gaps simultaneously, giving rise to a critical theory that mixes strong interactions with mutual statistics. An effective U(1) $\times$ U(1) gauge theory with a mutual Chern-Simons term at level $k$ is proposed to describe the vicinity of the multicritical point for $k \geq 4$. We argue analytically that monopoles are irrelevant in the IR CFT and compute the scaling dimensions of the leading duality-symmetric/anti-symmetric operators. In the large $k$ limit, these scaling dimensions approach $3 - ν_{\rm XY}^{-1}$ as $1/k^2$, where $ν_{\rm XY}$ is the correlation length exponent of the 3D XY model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_07941 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Analytic framework for self-dual criticality in $\mathbb{Z}_k$ gauge theory with matter Shi, Zhengyan Darius Chatterjee, Arkya Strongly Correlated Electrons Statistical Mechanics High Energy Physics - Theory We study the putative multicritical point in 2+1D $\mathbb{Z}_k$ gauge theory where the Higgs and confinement transitions meet. The presence of an $e$-$m$ duality symmetry at this critical point forces anyons with nontrivial braiding to close their gaps simultaneously, giving rise to a critical theory that mixes strong interactions with mutual statistics. An effective U(1) $\times$ U(1) gauge theory with a mutual Chern-Simons term at level $k$ is proposed to describe the vicinity of the multicritical point for $k \geq 4$. We argue analytically that monopoles are irrelevant in the IR CFT and compute the scaling dimensions of the leading duality-symmetric/anti-symmetric operators. In the large $k$ limit, these scaling dimensions approach $3 - ν_{\rm XY}^{-1}$ as $1/k^2$, where $ν_{\rm XY}$ is the correlation length exponent of the 3D XY model. |
| title | Analytic framework for self-dual criticality in $\mathbb{Z}_k$ gauge theory with matter |
| topic | Strongly Correlated Electrons Statistical Mechanics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2407.07941 |