The c-d conjecture

Understand

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.