  We study 2+1 dimensional massless Dirac fermions and bosons coupled to a U(1)
gauge field as a model for underdoped cuprates. We find that the uniform
susceptibility and the specific heat coefficient are logarithmically enhanced
(compared to linear-in-T behavior) due to the fluctuation of transverse gauge
field which is the only massless mode at finite boson density. We analyze
existing data, and find good agreement in the spin gap phase. Within our
picture, the drop of the susceptibility below the superconducting T_c arises
from the suppression of gauge fluctuations.
