492 research outputs found
The periodic sl(2|1) alternating spin chain and its continuum limit as a bulk Logarithmic Conformal Field Theory at c=0
The periodic sl(2|1) alternating spin chain encodes (some of) the properties
of hulls of percolation clusters, and is described in the continuum limit by a
logarithmic conformal field theory (LCFT) at central charge c=0. This theory
corresponds to the strong coupling regime of a sigma model on the complex
projective superspace , and the spectrum of critical exponents can be
obtained exactly. In this paper we push the analysis further, and determine the
main representation theoretic (logarithmic) features of this continuum limit by
extending to the periodic case the approach of [N. Read and H. Saleur, Nucl.
Phys. B 777 316 (2007)]. We first focus on determining the representation
theory of the finite size spin chain with respect to the algebra of local
energy densities provided by a representation of the affine Temperley-Lieb
algebra at fugacity one. We then analyze how these algebraic properties carry
over to the continuum limit to deduce the structure of the space of states as a
representation over the product of left and right Virasoro algebras. Our main
result is the full structure of the vacuum module of the theory, which exhibits
Jordan cells of arbitrary rank for the Hamiltonian.Comment: 69pp, 8 fig
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