The genus-zero bootstrap of chiral vertex operators in Liouville theory

Cremmer, E.; Gervais, Jean‐Loup; Roussel, Jean

doi:10.1016/0550-3213(94)90620-3

Cited by 24 publications

(79 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For this purpose, the expression Eq.2.8 is more handy, since the fusion properties of the ξ fields are determined by their quantum group structure [7,19]. One has, on the unit circle, 24) where (2)) (see, e.g.…”

Section: The Liouville Fields With Positive Quantum-group Spinsmentioning

confidence: 99%

Gravity-matter couplings from Liouville theory

Gervais¹

1993

Nuclear Physics B

Self Cite

View full text Add to dashboard Cite

The three-point functions for minimal models coupled to gravity are derived in the operator approach to Liouville theory which is based on its U q (sl(2)) quantum group structure. The gravity-matter coupling is formulated by treating the latter as a continuation of the former. The result is very simple, and shown to agree with matrix-model calculations on the sphere. The precise definition of the corresponding cosmological constant is given in the operator solution of the quantum Liouville theory. It is shown that the symmetry between quantum-group spins J and −J − 1 previously put forward by the author is the explanation of the continuation in the number of screening operators discovered by Goulian and Li. Contrary to the previous discussions of this problem, the present approach clearly separates the emission operators for each leg. This clarifies the structure of the dressing by gravity. It is shown, in particular that the end points are not treated on the same footing as the mid point. Since the outcome is completely symmetric this suggests the possibility of a picture-changing mechanism.

show abstract

Section: The Liouville Fields With Positive Quantum-group Spinsmentioning

confidence: 99%

Gravity-matter couplings from Liouville theory

Gervais¹

1993

Nuclear Physics B

Self Cite

View full text Add to dashboard Cite

show abstract

“…As is well known [11], the continuation of the ground state expectation value I m is essentially given by a q-6j-symbol, and the explicit formulae were determined in ref. [8] (The general result is summarized in appendix A). In ref.…”

Section: Some Background Materialsmentioning

confidence: 99%

“…The only difference to the positive half-integer spin case, which was completely analyzed in ref. [8], is that the J 12 -sum now extends to −m 1 −m 2 instead of |J 1 −J 2 |. Indeed, the positivity of the screening numbers appearing in the braiding matrix leads via the Moore-Seiberg relation to the positivity of the screening numbers n 1 = J 1 + m 1 , n 2 = J 2 + m 2 , p 1,2 = J 1 + J 2 − J 12 , n = J 12 + m 1 + m 2 of the fusion matrix.…”

Section: Closure By Fusionmentioning

confidence: 99%

“…In section 4, we consider both screening charges together. The corresponding quantum group structure U q (sl(2)) ⊙ U q (sl (2)) is known [8] to be given by a sort of graded tensor product in the degenerate case, where the primary fields of spins J and J are of the type (2 J + 1, 2J + 1) in the BPZ classification. This is because the fields of type (1, 2J + 1) field commute with those of type (2 J + 1, 1) up to a simple phase.…”

Section: Introductionmentioning

confidence: 99%

“…The most spectacular success produced so far by the algebraic method was the discovery of the underlying quantum group symmetry [1] [2] [6], which had remained completely invisible in the other approaches. Until recent times, the main technical tool in this framework was the detailed study of the Virasoro null vector equations and their monodromy properties [1]- [9], which in turn are related to representations of the U q (sl(2)) quantum group with positive half-integer spins [8] [9]. More precisely, one finds that a subset of the observables of the theory -the positive integer powers of the inverse square root of the metric -are described by chiral vertex operators which are degenerate fields in the sense of BPZ [13].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Quantum group structure and local fields in the algebraic approach to 2D gravity

Schnittger

1995

Theor Math Phys

View full text Add to dashboard Cite

This review contains a summary of work by J.-L. Gervais and the author on the operator approach to 2d gravity. Special emphasis is placed on the construction of local observables -the Liouville exponentials and the Liouville field itself -and the underlying algebra of chiral vertex operators. The double quantum group structure arising from the presence of two screening charges is discussed and the generalized algebra and field operators are derived. In the last part, we show that our construction gives rise to a natural definition of a quantum tau function, which is a noncommutative version of the classical group-theoretic representation of the Liouville fields by Leznov and Saveliev.

show abstract

Quantum mechanical quantum group in two-dimensional gravity

Gervais

Strings and Symmetries

View full text Add to dashboard Cite

The genus-zero bootstrap of chiral vertex operators in Liouville theory

Cited by 24 publications

References 28 publications

Gravity-matter couplings from Liouville theory

Gravity-matter couplings from Liouville theory

Quantum group structure and local fields in the algebraic approach to 2D gravity

Quantum mechanical quantum group in two-dimensional gravity

Contact Info

Product

Resources

About