Liouville Theory as a Model for Prelocalized States in Disordered Conductors

Ian I. Kogan; C. Mudry; A. M. Tsvelik

doi:10.1103/physrevlett.77.707

Liouville Theory as a Model for Prelocalized States in Disordered Conductors

Physical Review Letters ◽

10.1103/physrevlett.77.707 ◽

1996 ◽

Vol 77 (4) ◽

pp. 707-710 ◽

Cited By ~ 74

Author(s):

Ian I. Kogan ◽

C. Mudry ◽

A. M. Tsvelik

Keyword(s):

Liouville Theory

Download Full-text

Application of the Fractional Sturm–Liouville Theory to a Fractional Sturm–Liouville Telegraph Equation

Complex Analysis and Operator Theory ◽

10.1007/s11785-021-01125-3 ◽

2021 ◽

Vol 15 (5) ◽

Author(s):

M. Ferreira ◽

M. M. Rodrigues ◽

N. Vieira

Keyword(s):

Telegraph Equation ◽

Liouville Theory ◽

Sturm Liouville

Download Full-text

Higher rank FZZ-dualities

Journal of High Energy Physics ◽

10.1007/jhep02(2021)140 ◽

2021 ◽

Vol 2021 (2) ◽

Author(s):

Thomas Creutzig ◽

Yasuaki Hikida

Keyword(s):

Field Theory ◽

Reduction Method ◽

Operator Algebras ◽

The Self ◽

Liouville Theory ◽

Conformal Field ◽

Self Duality ◽

Higher Rank ◽

Corner Vertex ◽

Liouville Field Theory

Abstract 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 $$ \mathfrak{sl}(2)/\mathfrak{u}(1) $$ sl 2 / u 1 coset and sine-Liouville theory. In a previous work, a proof of the FZZ-duality was provided by applying the reduction method from $$ \mathfrak{sl}(2) $$ sl 2 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 $$ \mathfrak{sl}\left(N+1\right)/\left(\mathfrak{sl}(N)\times \mathfrak{u}(1)\right) $$ sl N + 1 / sl N × u 1 and investigate the equivalence to a theory with an $$ \mathfrak{sl}\left(N+\left.1\right|N\right) $$ sl N + 1 N structure. We derive the duality explicitly for N = 2, 3 by applying recent works on the reduction method extended for $$ \mathfrak{sl}(N) $$ sl N 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 Y0,N,N+1[ψ] and YN,0,N+1[ψ−1].

Download Full-text

Geometrical four-point functions in the two-dimensional critical Q-state Potts model: the interchiral conformal bootstrap

Journal of High Energy Physics ◽

10.1007/jhep12(2020)019 ◽

2020 ◽

Vol 2020 (12) ◽

Author(s):

Yifei He ◽

Jesper Lykke Jacobsen ◽

Hubert Saleur

Keyword(s):

Potts Model ◽

Correlation Functions ◽

Liouville Theory ◽

Analytical Determination ◽

Conformal Weight ◽

Two Dimensional ◽

Conformal Blocks ◽

Conformal Bootstrap ◽

Point Correlation

Abstract Based on the spectrum identified in our earlier work [1], we numerically solve the bootstrap to determine four-point correlation functions of the geometrical connectivities in the Q-state Potts model. Crucial in our approach is the existence of “interchiral conformal blocks”, which arise from the degeneracy of fields with conformal weight hr,1, with r ∈ ℕ*, and are related to the underlying presence of the “interchiral algebra” introduced in [2]. We also find evidence for the existence of “renormalized” recursions, replacing those that follow from the degeneracy of the field $$ {\Phi}_{12}^D $$ Φ 12 D in Liouville theory, and obtain the first few such recursions in closed form. This hints at the possibility of the full analytical determination of correlation functions in this model.

Download Full-text