Liouville theory revisited

By J. Teschner. 2001

475 citations recorded by the source corpus.

We try to develop a coherent picture of Liouville theory as a two-dimensional conformal field theory that takes into account the perspectives of the path-integral approach, bootstrap, canonical quantization and the operator approach. To do this, we need to develop further some of these approaches. This includes in particular the construction of general exponential field operators from a set of covariant chiral operators. The latter are shown to satisfy braid relations that allow one to prove the locality of the former.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/b3e94be3ee586aa909d3f25ea1143389811f656d

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Citations in the corpus

The tachyon at the end of the universe (2005, background): “from Liouville theory (for a review see [15,16,17]).”
A New Hat For The c=1 Matrix Model (2003, unknown): “[48]) Vα = S(α)VQ−α S(α) = ( πμ0γ(b (2)) )−(Q−2α)/b Γ ( 1 b (Q− 2α) )”
A paradigm of open/closed duality Liouville D-branes and the Kontsevich model (2003, background): “[15, 14, 9] and references therein), and it is largely thanks to this progress that we shall be able to carry our analysis.”
Rolling tachyons from Liouville theory (2003, unknown): “[21] for a more detailed discussion), namely by the factor R(α), i.”
H3+-WZNW correlators from Liouville theory (2005, methodology): “At the moment , it is Liouville theory which is by far the best understood example of an interacting confo rmal field theory with a continuous set of primary fields, see [4, 5, 6] and references therein.”
The Schwarzian theory — origins (2018, unknown): “c measure again into the canonical one: A00(˙) ^A0(˙) A0(˙)2 B00(˙) ^B0(˙) B0(˙)2 = ˇ F(˙) ^˚ F(˙); (2.19) proving that the transformation (˚;ˇ ˚) !(˚ F;ˇ F) is canonical in eld space (see e.g. [45] and references therein). The Hamiltonian gets transformed into the free-eld one: H= c 48ˇ Z ˇ 0 d˙ ˇ”
Chern-Simons theory and S-duality (2011, background): “While S-duality of the Teichmüller and Liouville algebras was noticed2 some time ago [18, 24], S-duality for ÂCS ~ (C) in Chern-Simons theory appeared only recently, for the case C = T 2, in [11].”
Quantum Riemann Surfaces in Chern-Simons Theory (2011, unknown): “The appearance of σ-duality in Chern-Simons theory can be considered a 3d lift of the well-known 2d S-duality, often written b↔ b−1 in quantum Teichmüller [58, 82, 80] and Liouville [89] theories.”
Quantization of the Hitchin moduli spaces, Liouville theory, and the geometric Langlands correspondence I (2010, methodology): “While cut systems can be used to label boundary components in∂Mg,n, one may parameterize boundary components ∂σTg,n of the Teichmüller spaceTg,n with the help of markingsσ.”
Liouville Correlation Functions from Four-Dimensional Gauge Theories (2009, background): “More details can be found in the reviews [21, 22].”
Quantum Groups and Quantum Cohomology (2012, methodology): “ −αn(γ). (13.16) Thus of the four operators R±± only one is really nontrivial. Also, we note η= 0 ⇒R+− = R−− . (13.17) 13.4.4 The operator R−+ is known as the reﬂection operator in Liouville CFT, see [107], while we will identify R(u) with the operator R+− for H= H· G(C 2) h 1 detC2 i in Section 14.”
Solving the Schwarzian via the conformal bootstrap (2017, methodology): “and following [25] we use the following integral representation of the asymmetric 6j-symbol { α1 α2 αs α3 ᾱ4 αt }an”
Liouville Field Theory — A decade after the revolution (2004, methodology): “3 Semiclassical Liouville Theory In this section, we quantize the Liouville theory semiclassically [36], [1], [37], [11] (See [38, 39], [40] for other quantization approaches.”
Three-dimensional Bondi-Metzner-Sachs invariant two-dimensional field theories as the flat limit of Liouville theory (2012, unknown): “[1, 2, 3] for reviews).”
Dilaton gravity in two-dimensions (2002, background): “Recently again interesting developments should be noted in Liouville gravity [151, 406].”
LSZ in LST (2004, unknown): “[47]): Vα =RαVQ−α, Rα = − μ Q−2α b Γ(−(1)b (Q− 2α))Γ(−b(Q− 2α)) Γ( 1b (Q− 2α))Γ(b(Q− 2α)) , (8.”
The Annular Report on Non-Critical String Theory (2003, background): “In spite of all the progress the Liouville theory has inspired over the years, an understanding of its detailed properties – for instance, a prescription to compute correlation functions – is of relatively recent vintage [34, 35](3) (for a review and further references, see [40]).”