Explicit finite-n lattice correlators for dense polymers on a cylinder are computed via Temperley-Lieb algebra and shown to match ratios of c=-2 CFT correlators involving boundary fields of dimensions -1/8 and 0, with non-abelian fusion.
Non-scalar operators for the Potts model in arbitrary dimension
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abstract
We investigate the operator content of the Q-state Potts model in arbitrary dimension, using the representation theory of the symmetric group. In particular we construct all possible tensors acting on N spins, corresponding to given symmetries under $S_Q$ and $S_N$, in terms of representations involving any Young diagram. These operators transform non-trivially under the group of spatial rotations, with a definite conformal spin. The two-point correlation functions are then computed, and their physical interpretation is given in terms of Fortuin-Kasteleyn clusters propagating between two neighbourhoods of each N spins. In two dimensions, we obtain analytically the critical exponent corresponding to each operator. In the simplest and physically most relevant cases, we confirm the values of the critical exponent and the conformal spin by numerical measurements, using both Monte Carlo simulations and transfer matrix diagonalisations. Our classification partially provides the structure of Jordan cells of the dilatation operator in arbitrary dimensions, which in turn gives rise to logarithmic correlation functions.
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UNVERDICTED 2representative citing papers
Torus one-point functions of primary fields in critical loop models are infinite sums of conformal blocks whose coefficients are products of double Gamma functions and polynomials in the loop weight, obtained via numerical bootstrap from sphere four-point functions at different central charge.
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Logarithmic correlation functions for critical dense polymers on the cylinder
Explicit finite-n lattice correlators for dense polymers on a cylinder are computed via Temperley-Lieb algebra and shown to match ratios of c=-2 CFT correlators involving boundary fields of dimensions -1/8 and 0, with non-abelian fusion.
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Torus one-point functions in critical loop models
Torus one-point functions of primary fields in critical loop models are infinite sums of conformal blocks whose coefficients are products of double Gamma functions and polynomials in the loop weight, obtained via numerical bootstrap from sphere four-point functions at different central charge.