From the sine-Gordon field theory to the Kardar-Parisi-Zhang growth equation

Abstract

We unveil a remarkable connection between the sine-Gordon quantum field theory and the Kardar-Parisi-Zhang (KPZ) growth equation. We find that the non-relativistic limit of the two point correlation function of the sine-Gordon theory is related to the generating function of the height distribution of the KPZ field with droplet initial conditions, i.e. the directed polymer free energy with two endpoints fixed. As shown recently, the latter can be expressed as a Fredholm determinant which in the large time separation limit converges to the GUE Tracy-Widom cumulative distribution. Possible applications and extensions are discussed.

6 pages

References in corpus (10)

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• Growing interfaces uncover universal fluctuations behind scale invariance
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• Correlation functions of the one-dimensional attractive Bose gas
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Cited by in corpus (10)

• The inverse scattering of the Zakharov-Shabat system solves the weak noise theory of the Kardar-Parisi-Zhang equation
• Generalized Hydrodynamics of the attractive Non-Linear Schroedinger Equation
• Half-space stationary Kardar-Parisi-Zhang equation
• Probing the large deviations of the Kardar-Parisi-Zhang equation at short time with an importance sampling of directed polymers in random media
• Delta-Bose gas on a half-line and the KPZ equation: boundary bound states and unbinding transitions
• Dynamic criticality far-from-equilibrium: one-loop flow of Burgers-Kardar-Parisi-Zhang systems with broken Galilean invariance
• Log-Gamma directed polymer with fixed endpoints via the replica Bethe Ansatz
• Exactly solvable models of growing interfaces and lattice gases: the Arcetri models, ageing and logarithmic sub-ageing
• From Kardar-Parisi-Zhang scaling to soliton proliferation in Josephson junction arrays
• Quantum quenches in the sinh-Gordon and Lieb-Liniger models