Novel triangle relation and absence of tachyons in Liouville string field theory

Gervais, Jean‐Loup; Neveu, A.

doi:10.1016/0550-3213(84)90469-3

Cited by 329 publications

(260 citation statements)

References 10 publications

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“…Denote by C the central charge of gravity. The standard screening charges −α ± of the Liouville theory [17,18] are such that…”

Section: The Liouville Fields With Positive Quantum-group Spinsmentioning

confidence: 99%

“…At an intuitive level, the correspondence between φ 1 and φ 2 may be understood from the fact that the Verma modules, which they generate, coincide since the highest weights only depend upon (p (1) 0 ) 2 = (p (2) 0 ) 2 . The chiral family is built up [17,25,26,5,27] from the following operators is such that ψ j and ψ j are solutions of the equations [24,17] − d 2 ψ j (σ)…”

Section: A Appendixmentioning

confidence: 99%

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Gravity-matter couplings from Liouville theory

Gervais¹

1993

Nuclear Physics B

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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.

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“…Denote by C the central charge of gravity. The standard screening charges −α ± of the Liouville theory [17,18] are such that…”

Section: The Liouville Fields With Positive Quantum-group Spinsmentioning

confidence: 99%

Section: A Appendixmentioning

confidence: 99%

Gravity-matter couplings from Liouville theory

Gervais¹

1993

Nuclear Physics B

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“…The same classical dynamical YB equation appears in other contexts [25,26,27], too, and has recently received lot of attention [21,23,28,29].…”

Section: Elements Of H and Their Poisson Bracketsmentioning

confidence: 98%

“…Applying this to the classical G-symmetry studied in sec. 3.5, we can thus find a map, 25) whereΓ :M chir → G * is given by (3.96), such that m(Γ) satisfies (5.24) with respect to the standard PL structure. The resulting G * -valued momentum map then generates a PL action on the phase spaceM chir as outlined above.…”

Section: Exchange R-matrices With Poisson-lie Symmetrymentioning

confidence: 99%

Chiral extensions of the WZNW phase space, Poisson–Lie symmetries and groupoids

Balog

Fehér²,

Palla

2000

Nuclear Physics B

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The chiral WZNW symplectic form Ω ρ chir is inverted in the general case. Thereby a precise relationship between the arbitrary monodromy dependent 2-form appearing in Ω ρ chir and the exchange r-matrix that governs the Poisson brackets of the group valued chiral fields is established. The exchange r-matrices are shown to satisfy a new dynamical generalization of the classical modified Yang-Baxter (YB) equation and Poisson-Lie (PL) groupoids are constructed that encode this equation analogously as PL groups encode the classical YB equation. For an arbitrary simple Lie group G, exchange r-matrices are found that are in one-to-one correspondence with the possible PL structures on G and admit them as PL symmetries.

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“…This study and related investigations gave birth to the quantum group [7,17], which is a powerful tool in constructing trigonometric solutions to the YBE. Instead of the YBE, the DYBE [11,12,14] was required in order to define the elliptic quantum groups associated with elliptic solutions to the YBE.…”

Section: Introductionmentioning

confidence: 99%

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Shibukawa¹

2005

Internat. Math. Res. Notices

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Abstract. In this work, we propose and investigate dynamical YangBaxter maps, some of which produce solutions to the quantum dynamical Yang-Baxter equation. Suppose that L is a loop and a group. If their unit elements coincide, then L gives birth to a bijective dynamical Yang-Baxter map from L × L to L × L whose dynamical parameter belongs to L. The above group L is abelian if and only if the corresponding dynamical Yang-Baxter map satisfies the unitary condition.

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Novel triangle relation and absence of tachyons in Liouville string field theory

Cited by 329 publications

References 10 publications

Gravity-matter couplings from Liouville theory

Gravity-matter couplings from Liouville theory

Chiral extensions of the WZNW phase space, Poisson–Lie symmetries and groupoids

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