## Adiabatic corrections to holographic entanglement in thermofield doubles and confining ground states

16 Sep 2016  ·  Marolf Donald, Wien Jason ·

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 \${\mathbb R}^{d-1}\$ base... Such examples respect an \${\mathbb R}^{d-2}\$ Euclidean symmetry. Treating the \$S^1\$ 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 \$|x - x_0| \le 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 \$L_{crit}\$ for \$d \le 3\$ but increase \$L_{crit}\$ for \$d\ge4\$. This means that, while for general \$L > L_{crit}\$ they significantly increase the mutual information of opposing slabs as one would expect, for \$d\ge 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. read more

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High Energy Physics - Theory