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The c-d conjecture
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The c-d conjecture
abstract
We conjecture a relation between the local dimension $d$ of a local nearest-neighbor critical Hamiltonian in one spatial dimension and the maximum central charge, $c_{\text{max}}$, that it can yield. Specifically, we propose that $c_{\text{max}} \leq d-1$, establishing a link between the short-distance lattice realization of a model and its emerging long-distance entanglement properties. This inequality can be viewed as a general form of a $c$-theorem establishing the reduction of effective degrees of freedom between the UV lattice and the IR conformal field theory. We support this conjecture with numerous examples.
Forward citations
Cited by 1 Pith paper
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A systematic search for conformal field theories in very small spaces
A symmetry-free entropy search on four-site states recovers known CFTs and yields unclassified candidate CFTs with 1<c<2.
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