Decomposition of $\mathcal{N}=1$ superconformal minimal models and their fractional quantum Hall wavefunctions
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866909978226327552 |
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| author | Hu, Yichen Ning, Sirui Zhou, Yehao |
| author_facet | Hu, Yichen Ning, Sirui Zhou, Yehao |
| contents | $\mathcal{N}=1$ superconformal minimal models are the first series of unitary conformal field theories (CFTs) extending beyond Virasoro algebra. Using coset constructions, we characterize CFTs in $\mathcal{N}=1$ superconformal minimal models using combinations of a parafermion theory, an Ising theory and a free boson theory. Supercurrent operators in the original theory also becomes sums of operators from each constituent theory. If we take our $\mathcal{N}=1$ superconformal theories as the neutral part of the edge theory of a fractional quantum Hall state, we present a systematic way of calculating its ground state wavefunction using free field methods. Each ground state wavefunction is known previously as a sum of polynomials with distinct clustering behaviours. Based on our decomposition, we find explicit expressions for each summand polynomial. A brief generalization to $S_3$ minimal models using coset construction is also included. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_10107 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Decomposition of $\mathcal{N}=1$ superconformal minimal models and their fractional quantum Hall wavefunctions Hu, Yichen Ning, Sirui Zhou, Yehao High Energy Physics - Theory Strongly Correlated Electrons Mathematical Physics $\mathcal{N}=1$ superconformal minimal models are the first series of unitary conformal field theories (CFTs) extending beyond Virasoro algebra. Using coset constructions, we characterize CFTs in $\mathcal{N}=1$ superconformal minimal models using combinations of a parafermion theory, an Ising theory and a free boson theory. Supercurrent operators in the original theory also becomes sums of operators from each constituent theory. If we take our $\mathcal{N}=1$ superconformal theories as the neutral part of the edge theory of a fractional quantum Hall state, we present a systematic way of calculating its ground state wavefunction using free field methods. Each ground state wavefunction is known previously as a sum of polynomials with distinct clustering behaviours. Based on our decomposition, we find explicit expressions for each summand polynomial. A brief generalization to $S_3$ minimal models using coset construction is also included. |
| title | Decomposition of $\mathcal{N}=1$ superconformal minimal models and their fractional quantum Hall wavefunctions |
| topic | High Energy Physics - Theory Strongly Correlated Electrons Mathematical Physics |
| url | https://arxiv.org/abs/2303.10107 |