科研之友
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摘要
We study entanglement in states of holographic CFTs defined by Euclidean path integrals over geometries with slowly varying metrics. In particular, our CFT spacetimes have S-1 fibers whose size b varies along one direction (x) of an Rd-1 base. Such examples respect an Rd-2 Euclidean symmetry. Treating the S1 direction as time leads to a thermofield double state on a spacetime with adiabatically varying redshift, while treating another direction as time leads to a confining ground state with slowly varying confinement scale. In both contexts the entropy of slab-shaped regions defined by vertical bar x - x(0)vertical bar <= L exhibits well-known phase transitions at length scales L = L-crit characterizing the CFT entanglements. For the thermofield double, the numerical coefficients governing the effect of variations in b(x) on the transition are surprisingly small and exhibit an interesting change of sign: gradients reduce Lcrit for d <= 3 but increase L-crit for d >= 4. This means that, while for general L > L-crit they significantly increase the mutual information of opposing slabs as one would expect, for d >= 4 gradients cause a small decrease near the phase transition. In contrast, for the confining ground states gradients always decrease L-crit, with the effect becoming more pronounced in higher dimensions.
- 出版日期2016-9-12
