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Bibliographic record
Abstract
A bstract We examine strong/weak dualities in two dimensional conformal field theories by generalizing the Fateev-Zamolodchikov-Zamolodchikov (FZZ-)duality between Witten’s cigar model described by the $$ \mathfrak{sl}(2)/\mathfrak{u}(1) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>sl</mml:mi> <mml:mfenced> <mml:mn>2</mml:mn> </mml:mfenced> <mml:mo>/</mml:mo> <mml:mi>u</mml:mi> <mml:mfenced> <mml:mn>1</mml:mn> </mml:mfenced> </mml:math> coset and sine-Liouville theory. In a previous work, a proof of the FZZ-duality was provided by applying the reduction method from $$ \mathfrak{sl}(2) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>sl</mml:mi> <mml:mfenced> <mml:mn>2</mml:mn> </mml:mfenced> </mml:math> Wess-Zumino-Novikov-Witten model to Liouville field theory and the self-duality of Liouville field theory. In this paper, we work with the coset model of the type $$ \mathfrak{sl}\left(N+1\right)/\left(\mathfrak{sl}(N)\times \mathfrak{u}(1)\right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>sl</mml:mi> <mml:mfenced> <mml:mrow> <mml:mi>N</mml:mi> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:mfenced> <mml:mo>/</mml:mo> <mml:mfenced> <mml:mrow> <mml:mi>sl</mml:mi> <mml:mfenced> <mml:mi>N</mml:mi> </mml:mfenced> <mml:mo>×</mml:mo> <mml:mi>u</mml:mi> <mml:mfenced> <mml:mn>1</mml:mn> </mml:mfenced> </mml:mrow> </mml:mfenced> </mml:math> and investigate the equivalence to a theory with an $$ \mathfrak{sl}\left(N+\left.1\right|N\right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>sl</mml:mi> <mml:mfenced> <mml:mrow> <mml:mi>N</mml:mi> <mml:mo>+</mml:mo> <mml:mfenced> <mml:mn>1</mml:mn> </mml:mfenced> <mml:mi>N</mml:mi> </mml:mrow> </mml:mfenced> </mml:math> structure. We derive the duality explicitly for N = 2 , 3 by applying recent works on the reduction method extended for $$ \mathfrak{sl}(N) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>sl</mml:mi> <mml:mfenced> <mml:mi>N</mml:mi> </mml:mfenced> </mml:math> and the self-duality of Toda field theory. Our results can be regarded as a conformal field theoretic derivation of the duality of the Gaiotto-Rapčák corner vertex operator algebras Y 0 ,N,N +1 [ ψ ] and Y N, 0 ,N +1 [ ψ − 1 ].
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it