  Glasses at low temperature fluctuate around their inherent states; glassy
anomalies reflect the structure of these states. Recently there have been
numerous observations of long-range stress correlations in glassy materials,
from supercooled liquids to colloids and granular materials, but without a
common explanation. Herein it is shown, using a field theory of inherent
states, that long-range stress correlations follow from mechanical equilibrium
alone, with explicit predictions for stress correlations in 2 and 3 dimensions.
`Equations of state' relating fluctuations to imposed stresses are derived, as
well as field equations that fix the spatial structure of stresses in arbitrary
geometries. Finally, a new holographic quantity in 3D amorphous systems is
identified.
