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Liouville Field Theory of Fluctuating Loops

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arxiv cond-mat/9703113 v1 pith:FF65XJWP submitted 1997-03-12 cond-mat.stat-mech hep-th

J. Kondev (Brown University) This is my paper · ORCID
classification cond-mat.stat-mechhep-th
keywords criticalfieldconformalfluctuatinglatticeliouvilleloopsmethod
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Effective field theories of two-dimensional lattice models of fluctuating loops are constructed by mapping them onto random surfaces whose large scale fluctuations are described by a Liouville field theory. This provides a geometrical view of conformal invariance in two-dimensional critical phenomena and a method for calculating critical properties of loop models exactly. As an application of the method, the conformal charge and critical exponents for two mutually excluding Hamiltonian walks on the square lattice are calculated.

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    Nodal lines in 2D active scalar turbulence are proposed to be domain walls between constant-flux patches, described by a Liouville conformal field theory whose central charge is set by a fractional winding number matc...

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