Verlinde lines, anyon permutations and commutant pairs inside $E_{8,1}$ CFT
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| Formato: | Preprint |
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2026
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| author | Umasankar, Naveen Balaji Das, Arpit |
| author_facet | Umasankar, Naveen Balaji Das, Arpit |
| contents | We develop a defect-theoretic refinement of meromorphic 2d CFTs in which the ordinary torus partition function -- often just the vacuum character -- does not reveal how states organize under symmetry lines. Our central proposal is an \emph{equatorial projection} framework: from a commutant decomposition into commuting rational chiral algebras with categories $\mathcal{C}$ and $\widetilde{\mathcal{C}}$, we encode genus-one couplings by a non-negative integer matrix $M$ pairing characters and satisfying modular intertwiner relations. Invertible topological defect lines act directly on this gluing data (Verlinde lines diagonally via $S$-matrix eigenvalues, and anyon-permuting lines by braided-autoequivalence permutations), making modular covariance of defect amplitudes automatic and sharply distinguishing insertions that yield genuine modular invariants from those defining consistent non-holomorphic interfaces. We further show that the \emph{replacement rules} of \cite{Hegde:2021sdm, Lin:2019hks} arise as equatorial projections of defect actions, and we extend these constructions beyond two-character examples by systematically treating three-character commutant pairs in the $E_{8,1}$ theory. The unique $c=8$ meromorphic CFT $E_{8,1}$ serves as a universal testbed, producing new defect partition functions and clarifying the roles of $\mathrm{Pic}(\mathcal{C})$ and $\mathrm{Aut}^{\mathrm{br}}(\mathcal{C})$. Finally, we outline extensions to higher central charges (e.g.\ $c=32,40$), yielding modular-invariant non-meromorphic theories beyond the $c=24$ Schellekens landscape \cite{Schellekens:1992db} as defect/interface descendants of meromorphic parents. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_02700 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Verlinde lines, anyon permutations and commutant pairs inside $E_{8,1}$ CFT Umasankar, Naveen Balaji Das, Arpit High Energy Physics - Theory Mathematical Physics We develop a defect-theoretic refinement of meromorphic 2d CFTs in which the ordinary torus partition function -- often just the vacuum character -- does not reveal how states organize under symmetry lines. Our central proposal is an \emph{equatorial projection} framework: from a commutant decomposition into commuting rational chiral algebras with categories $\mathcal{C}$ and $\widetilde{\mathcal{C}}$, we encode genus-one couplings by a non-negative integer matrix $M$ pairing characters and satisfying modular intertwiner relations. Invertible topological defect lines act directly on this gluing data (Verlinde lines diagonally via $S$-matrix eigenvalues, and anyon-permuting lines by braided-autoequivalence permutations), making modular covariance of defect amplitudes automatic and sharply distinguishing insertions that yield genuine modular invariants from those defining consistent non-holomorphic interfaces. We further show that the \emph{replacement rules} of \cite{Hegde:2021sdm, Lin:2019hks} arise as equatorial projections of defect actions, and we extend these constructions beyond two-character examples by systematically treating three-character commutant pairs in the $E_{8,1}$ theory. The unique $c=8$ meromorphic CFT $E_{8,1}$ serves as a universal testbed, producing new defect partition functions and clarifying the roles of $\mathrm{Pic}(\mathcal{C})$ and $\mathrm{Aut}^{\mathrm{br}}(\mathcal{C})$. Finally, we outline extensions to higher central charges (e.g.\ $c=32,40$), yielding modular-invariant non-meromorphic theories beyond the $c=24$ Schellekens landscape \cite{Schellekens:1992db} as defect/interface descendants of meromorphic parents. |
| title | Verlinde lines, anyon permutations and commutant pairs inside $E_{8,1}$ CFT |
| topic | High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2602.02700 |