  Effective gauge theories based on slave particle construction are widely used
to describe quantum number fractionalization in strongly correlated electron
systems. However, even setting aside the intense debates on the confinement
issue of the slave particles, there are still significant conflicts between
theory and experiment. In particular, a $T^{2/3}$ specific heat anomaly has
been predicted as the key signature of low-lying gauge fluctuation in a $U(1)$
spin liquid with a large spinon Fermi surface, which is however never observed.
Here we show that such an anomaly is actually an artifact of a Gaussian
approximation and is absent when the no double occupancy constraint on the
slave particles is strictly enforced. We also show that projective construction
based on slave particle representation provides a unified understanding on the
mechanism of spin fractionalization and the nonlocal nature of a physical
spinon in one and two dimensional spin liquids.
