Scale vs Conformal invariance from Entanglement Entropy

Abstract

For a generic conformal field theory (CFT) in four dimensions, the scale anomaly dictates that the universal part of entanglement entropy across a sphere (${\mathcal{C}}_{\text{univ}}(S^2)$) is positive. Based on this fact, we explore the consequences of assuming positive sign for ${\mathcal{C}}_{\text{univ}}(S^2)$ in a four dimensional scale invariant theory (SFT). In absence of a dimension two scalar operator ${\mathcal{O}}_2$ in the spectrum of a SFT, we show that this assumption suggests that SFT is a CFT. In presence of ${\mathcal{O}}_2$, we show that this assumption can fix the coefficient of the nonlinear coupling term $\int d^{4}x\sqrt{g}R{\mathcal{O}}_2$ to a conformal value.

6 pages, no figures

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