Liouville Field Theory — A decade after the revolution

By Y. Nakayama. 2004

395 citations recorded by the source corpus.

We review recent developments (up to January 2004) of the Liouville field theory and its matrix model dual. This review consists of three parts. In part I, we review the bosonic Liouville theory. After briefly reviewing the necessary background, we discuss the bulk structure constants (the DOZZ formula) and the boundary states (the FZZT brane and the ZZ brane). Various applications are also presented. In part II, we review the supersymmetric extension of the Liouville theory. We first discuss the bulk structure constants and the branes as in the bosonic Liouville theory, and then we present the matrix dual descriptions with some applications. In part III, the Liouville theory on unoriented surfaces is reviewed. After introducing the crosscap state, we discuss the matrix model dual description and the tadpole cancellation condition. This review also includes some original material such as the derivation of the conjectured dual action for the N = 2 Liouville theory from other known dualities and the comparison of the Liouville crosscap state with the c = 0 unoriented matrix model. This is based on my master’s thesis submitted to Department of Physics, Faculty of Science, University of Tokyo on January 2004.

Subfields: Condensed Matter Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/b30ec837ddc67ffb8530c3abfaa64cc5e731d8a2

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Citations in the corpus

Sachdev–Ye–Kitaev model as Liouville quantum mechanics (2016, neutral): “quantum mechanics in an exponential potential [5, 6, 7].”
Liouville Quantum Gravity on the Riemann Sphere (2014, methodology): “9), we obtain a rigorous derivation of the KPZ scaling laws (see [37,39,49] for physics references) Theorem 3.”
Critical Gaussian multiplicative chaos: Convergence of the derivative martingale (2012, methodology): “constructed a probabilistic and geometrical framework for Liouville quantum gravity and the so-called Knizhnik–Polyakov–Zamolodchikov (KPZ) equation [51], based on the two-dimensional Gaussian free field (GFF); see [23, 25, 26, 30, 38, 51, 61] and references therein.”
Liouville Correlation Functions from Four-Dimensional Gauge Theories (2009, background): “More details can be found in the reviews [21, 22].”
Thermodynamics of black holes in two (and higher) dimensions (2007, neutral): “Liouville Gravity a beαX eaX − 2b a+α e(a+α)X [75]”
The Resurgence of Instantons in String Theory (2011, background): “, (2)Of course these instantons also played a decisive role in many nonperturbative questions addressed within minimal string theory [5, 19] and were later precisely identified as D–brane configurations in [20].”
Static patch solipsism: conformal symmetry of the de Sitter worldline (2011, neutral): “[42] and references therein).”
H3+-WZNW correlators from Liouville theory (2005, background): “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.”
Phases of quantum gravity in AdS3 and linear dilaton backgrounds (2005, background): “[7,8] for reviews) and the Euclidean CFT on the cigar, SL(2, IR)/U(1).”
Analytic continuation of Liouville theory (2011, background): “Some relatively modern reviews on Liouville theory are [30, 31]; a much older one is [8].”