scholarly journals Seiberg-Witten equations and non-commutative spectral curves in Liouville theory

2013 ◽  
Vol 54 (2) ◽  
pp. 022306 ◽  
Author(s):  
Leonid Chekhov ◽  
Bertrand Eynard ◽  
Sylvain Ribault
Keyword(s):  
Liouville Theory ◽  
Spectral Curves

scholarly journals Spectral curves are transcendental

2021 ◽  
Vol 111 (1) ◽  
Author(s):  
H. W. Braden
Keyword(s):  
Spectral Curve ◽  
Spectral Curves ◽  
Arithmetic Properties ◽  
A Charge

AbstractSome arithmetic properties of spectral curves are discussed: the spectral curve, for example, of a charge $$n\ge 2$$ n ≥ 2 Euclidean BPS monopole is not defined over $$\overline{\mathbb {Q}}$$ Q ¯ if smooth.

scholarly journals Higher rank FZZ-dualities

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].

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

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.

scholarly journals Liouville Theory as a Model for Prelocalized States in Disordered Conductors

1996 ◽  
Vol 77 (4) ◽  
pp. 707-710 ◽  
Author(s):  
Ian I. Kogan ◽  
C. Mudry ◽  
A. M. Tsvelik
Keyword(s):  
Liouville Theory

Integration in Finite Terms: The Liouville Theory

1980 ◽  
Vol 53 (4) ◽  
pp. 195 ◽  
Author(s):  
Toni Kasper
Keyword(s):  
Liouville Theory

Solution of N=2 superconformal Liouville theory

1991 ◽  
Vol 255 (2) ◽  
pp. 230-236 ◽  
Author(s):  
H.C. Liao ◽  
P. Mansfield
Keyword(s):  
Liouville Theory

scholarly journals MICROSPECTROPHOTOMETRY OF NEWLY SYNTHESIZED STARCH IN SITU

1970 ◽  
Vol 18 (6) ◽  
pp. 439-449
Author(s):  
GEORGE E. WHEELER
Keyword(s):  
Absorption Maximum ◽  
In Vitro Studies ◽  
Phosphate Solution ◽  
Starch Digestion ◽  
Spectral Curves ◽  
Similarities And Differences

Many of the cells in stem sections of several Commelinaceae species synthesized much new starch when incubated in buffered 1% glucose 1-phosphate solution. The starch appeared in the cytoplasm rather than in the plastids. Although the starch I2-KI color was uniform within any one cell, there was considerable variation from cell to cell, even in the same section. The colors with I2-KI ranged from blue, through purples to magenta and mahogany. Tests with α-amylase and with β-amylase showed the starch to be amylose. Microspectrophotometrically determined extinction curves, based on the new starch in situ, varied with the visualized color. As expected, starch which stained blue with I2-KI had an absorption maximum in the orange-red wavelengths above 600 mµ; increasingly red I2-KI colors were characterized by shifts of the absorption maximum further into the shorter wavelengths. The course of new starch digestion by α-amylase and by β-amylase was followed visually and with the microspectrophotometer. Similarities and differences between these spectral curves and those published for in vitro studies are pointed out. The difficulties met with in using the microspectrophotometric method are discussed.

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