Polynomial energy bounds for type $F_4$ WZW-models

Bin Gui

备注：: 21 pages, updated to published version
发表信息：: Internat. J. Math., Vol. 31, No. 12 (2020)
DOI：: 10.1142/S0129167X20500962

英文摘要：

We prove that sufficiently many intertwining operators of type $F_4$ unitary affine VOAs satisfy polynomial energy bounds. This finishes the Wassermann type analysis of intertwining operators for all WZW-models.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

S and T matrices for the super $U(1,1)$ WZW model. Application to surgery and 3-manifold invariants based on the Alexander Conway polynomial

We carry on the study of the Alexander Conway invariant from the quantum field theory point of view started in \cite{RS91}. We first discuss in details $S$ and $T$ matrices for the $U(1,1)$ super WZW model and obtain, for the level $k$ an integer, new finite dimensional representations of the modular group. These have the remarkable property that some of the $S$ matrix elements are infinite. Moreover, typical and atypical representations as well as indecomposable blocks are mixed: truncation to maximally atypical representations, as advocated in some recent papers, is not consistent. The main …

1992-03-25hep-thmath.QA

Modular transformations of the elliptic hypergeometric functions, Macdonald polynomials, and the shift operator

We consider the space of elliptic hypergeometric functions of the sl_2 type associated with elliptic curves with one marked point. This space represents conformal blocks in the sl_2 WZW model of CFT. The modular group acts on this space. We give formulas for the matrices of the action in terms of values at roots of unity of Macdonald polynomials of the sl_2 type.

2002-10-14math.QA

Factorization algebras and abelian CS/WZW-type correspondences

We develop a method of quantization for free field theories on manifolds with boundary where the bulk theory is topological in the direction normal to the boundary and a local boundary condition is imposed. Our approach is within the Batalin-Vilkovisky formalism. At the level of observables, the construction produces a stratified factorization algebra that in the bulk recovers the factorization algebra developed by Costello and Gwilliam. The factorization algebra on the boundary stratum enjoys a perturbative bulk-boundary correspondence with this bulk factorization algebra. A central example i…

2021-06-29hep-thmath-phmath.AT

On the affine analogue of Jack's and Macdonald's polynomials

We define the analogue of Jack's (Jacobi) polynomials, which were defined for finite-dimensional root system by Heckman and Opdam as eigenfunctions of trigonometric Sutherland operator for the affine root system $\hat A_{n-1}$. In the affine case, we define the polynomials as eigenfunctions of "affine Sutherland operator", which is Calogero-Sutherland operator with elliptic potential plus the term involving derivative with respect to the modular parameter. We show that such polynomials can be constructed explicitly as traces of certain intertwiners for affine Lie algebra. Also, we define the q…

1995-01-24hep-thmath.QA

Spaces of coinvariants and fusion product I. From equivalence theorem to Kostka polynomials

The fusion rule gives the dimensions of spaces of conformal blocks in the WZW theory. We prove a dimension formula similar to the fusion rulefor spaces of coinvariants of affine Lie algebras g^. An equivalence of filtered spaces is established between spaces of coinvariants of two objects: highest weight g^-modules and tensor products of finite-dimensional evaluation representations of g\otimes\C[t]. In the sl_2 case we prove that their associated graded spaces are isomorphic to the spaces of coinvariants of fusion products, and that their Hilbert polynomials are the level-restricted Kostka po…

2002-10-08math.COmath.QAmath.RT

Schubert Calculus and Threshold Polynomials of Affine Fusion

We show how the threshold level of affine fusion, the fusion of Wess-Zumino-Witten (WZW) conformal field theories, fits into the Schubert calculus introduced by Gepner. The Pieri rule can be modified in a simple way to include the threshold level, so that calculations may be done for all (non-negative integer) levels at once. With the usual Giambelli formula, the modified Pieri formula deforms the tensor product coefficients (and the fusion coefficients) into what we call threshold polynomials. We compare them with the q-deformed tensor product coefficients and fusion coefficients that are rel…

2000-04-18hep-thmath.QA

更多相关论文收起更多论文

Traces of intertwining operators and Macdonald's polynomials

Let $Φ:V\to V\otimes U$ be an intertwining operator between representations of a simple Lie algebra (quantum group, affine Lie algebra). We define its generalized character to be the following function on the Cartan subalgebra with values in $U$: $χ_Φ(h)=\Tr_V (Φe^h)$. These generalized characters are a rich source of special functions, possessing many interesting properties; for example, they are common eigenfunctions of a family of commuting differential (difference) operators. We show that the special functions that can be obtained this way include Macdonald's polynomials of type $A$, and t…

1995-03-21hep-thmath.QAq-alg

手征共形场论中的融合与正性

Fusion and positivity in chiral conformal field theory

本研究通过基于有界局域顶点算子的新框架，证明WZW模型对应的共形网是有理的、其Jones-Wassermann子因子有有限指标，解决了长期公开问题，并拓展了相关应用范围。

2024-09-13math-phmath.MPmath.OA