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| Format: | Preprint |
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2024
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| Online-Zugang: | https://arxiv.org/abs/2412.10112 |
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| _version_ | 1866915334507724800 |
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| author | Gowdigere, Chethan N. Kala, Sachin Santara, Jagannath |
| author_facet | Gowdigere, Chethan N. Kala, Sachin Santara, Jagannath |
| contents | We study one-character CFTs obtained as one-character extensions of the tensor products of a single CFT $\mathcal{C}$. The motivation comes from the fact that $28$ of the $71$ CFTs in the Schelleken's list of $c = 24$ CFTs are such CFTs. We study for $\mathcal{C}$ : (i) any two-character WZW CFT with vanishing Wronskian index, (ii) the Ising CFT, (iii) the infinite class of $D_{r,1}$ CFTs and the $A_{4,1}$ CFT. The characters being $S$-invariant homogenous polynomials of the characters of $\mathcal{C}$, when organised in terms of a $S$-invariant basis, take compact forms allowing for closed form answers for high central charges. We find a $S$-invariant basis for each of the CFTs studied. As an example, one can find an explicit expression for the character of the monster CFT as a degree-$48$ polynomial of the characters of the Ising CFT. In some CFTs, some of the $S$-invariant polynomials of characters compute, after using the $q$-series of the characters, to a constant value. Hence, the characters of one-character extensions are more properly elements of the quotient ring of polynomials (of characters) with the ideal needed for the quotient, generated by $S$-invariant polynomials that compute to a constant. In some cases, we are able to rule out the existence of one-character extension CFTs. In other cases, we predict their existence. We are able to conjecture a discrete set of six and four infinite series of one-character extension CFTs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_10112 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Tensor Product CFTs and One-Character Extensions Gowdigere, Chethan N. Kala, Sachin Santara, Jagannath High Energy Physics - Theory Mathematical Physics We study one-character CFTs obtained as one-character extensions of the tensor products of a single CFT $\mathcal{C}$. The motivation comes from the fact that $28$ of the $71$ CFTs in the Schelleken's list of $c = 24$ CFTs are such CFTs. We study for $\mathcal{C}$ : (i) any two-character WZW CFT with vanishing Wronskian index, (ii) the Ising CFT, (iii) the infinite class of $D_{r,1}$ CFTs and the $A_{4,1}$ CFT. The characters being $S$-invariant homogenous polynomials of the characters of $\mathcal{C}$, when organised in terms of a $S$-invariant basis, take compact forms allowing for closed form answers for high central charges. We find a $S$-invariant basis for each of the CFTs studied. As an example, one can find an explicit expression for the character of the monster CFT as a degree-$48$ polynomial of the characters of the Ising CFT. In some CFTs, some of the $S$-invariant polynomials of characters compute, after using the $q$-series of the characters, to a constant value. Hence, the characters of one-character extensions are more properly elements of the quotient ring of polynomials (of characters) with the ideal needed for the quotient, generated by $S$-invariant polynomials that compute to a constant. In some cases, we are able to rule out the existence of one-character extension CFTs. In other cases, we predict their existence. We are able to conjecture a discrete set of six and four infinite series of one-character extension CFTs. |
| title | Tensor Product CFTs and One-Character Extensions |
| topic | High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2412.10112 |