Correlation functions in Liouville theory

Goulian, Mark; Li, Miao

doi:10.1103/physrevlett.66.2051

Cited by 268 publications

(432 citation statements)

References 17 publications

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“…The Liouville correlation function can be obtained by integrating the contribution from the three-point function and the conformal block over the internal momenta. In this section, we explain how the integral representation (1.1) appears from the full correlation function, based on the discussion of [33,54].…”

Section: From Liouville Theory To Generalized Matrix Modelmentioning

confidence: 99%

Seiberg-Witten curve via generalized matrix model

Maruyoshi

Yagi

2011

J. High Energ. Phys.

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Abstract:We study the generalized matrix model which corresponds to the n-point toric Virasoro conformal block. This describes four-dimensional N = 2 SU(2) n gauge theory with circular quiver diagram by the AGT relation. We first verify that the generalized matrix model is obtained from the perturbative calculation of the Liouville correlation function. We then derive the Seiberg-Witten curve for N = 2 gauge theory as a spectral curve of the generalized matrix model.

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Section: From Liouville Theory To Generalized Matrix Modelmentioning

confidence: 99%

Seiberg-Witten curve via generalized matrix model

Maruyoshi

Yagi

2011

J. High Energ. Phys.

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“…Following [24], we decompose X = q +X where q is the zero mode of X. Then the q integral can be done exactly, yielding…”

Section: Bulk Correlatorsmentioning

confidence: 99%

Timelike boundary Liouville theory

2003

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The timelike boundary Liouville (TBL) conformal field theory consisting of a negative norm boson with an exponential boundary interaction is considered. TBL and its close cousin, a positive norm boson with a non-hermitian boundary interaction, arise in the description of the c = 1 accumulation point of c < 1 minimal models, as the worldsheet description of open string tachyon condensation in string theory and in scaling limits of superconductors with line defects. Bulk correlators are shown to be exactly soluble. In contrast, due to OPE singularities near the boundary interaction, the computation of boundary correlators is a challenging problem which we address but do not fully solve. Analytic continuation from the known correlators of spatial boundary Liouville to TBL encounters an infinite accumulation of poles and zeros. A particular contour prescription is proposed which cancels the poles against the zeros in the boundary correlator d(ω) of two operators of weight ω 2 and yields a finite result. A general relation is proposed between two-point CFT correlators and stringy Bogolubov coefficients, according to which the magnitude of d(ω) determines the rate of open string pair creation during tachyon condensation. The rate so obtained agrees at large ω with a minisuperspace analysis of previous work. It is suggested that the mathematical ambiguity arising in the prescription for analytic continuation of the correlators corresponds to the physical ambiguity in the choice of open string modes and vacua in a time dependent background. *

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“…In particular, using the approach outlined in Ref. [36] (see also [32,37]), it is possible to obtain Coulomb gas integral representations for f (−) i,0 (P, Q) at the poles P = i m √ n , m = 0, 1, 2 . .…”

Section: Short Distance Expansionmentioning

confidence: 99%

Boundary RG flow associated with the AKNS soliton hierarchy

Fateev

Lukyanov

2006

J. Phys. A: Math. Gen.

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We introduce and study an integrable boundary flow possessing an infinite number of conserving charges which can be thought of as quantum counterparts of the Ablowitz, Kaup, Newell and Segur Hamiltonians. We propose an exact expression for overlap amplitudes of the boundary state with all primary states in terms of solutions of certain ordinary linear differential equation. The boundary flow is terminated at a nontrivial infrared fixed point. We identify a form of whole boundary state corresponding to this fixed point.October 2005

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Correlation functions in Liouville theory

Cited by 268 publications

References 17 publications

Seiberg-Witten curve via generalized matrix model

Seiberg-Witten curve via generalized matrix model

Timelike boundary Liouville theory

Boundary RG flow associated with the AKNS soliton hierarchy

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