  Outbursts from active galactic nuclei (AGN) can inflate cavities in the
intracluster medium (ICM) of galaxy clusters and are believed to play the
primary role in offsetting radiative cooling in the ICM. However, the details
of how the energy from AGN feedback thermalizes to heat the ICM is not well
understood, partly due to the unknown composition and energetics of the
cavities. The Sunyaev-Zel'dovich (SZ) effect, a measure of the integrated
pressure along the line of sight, provides a means of measuring the thermal
contents of the cavities, to discriminate between thermal, nonthermal, and
other sources of pressure support. Here we report measurements of the SZ effect
at 30 GHz toward the galaxy cluster MS 0735.6+7421 (MS0735), using the Combined
Array for Research in Millimeter-wave Astronomy (CARMA). MS0735 hosts the most
energetic AGN outburst known and lobes of radio synchrotron emission coincident
with a pair of giant X-ray cavities $\sim 200$ across. Our CARMA maps show a
clear deficit in the SZ signal coincident with the X-ray identified cavities,
when compared to a smooth X-ray derived pressure model. We find that the
cavities have very little SZ-contributing material, suggesting that they are
either supported by very diffuse thermal plasma with temperature in excess of
hundreds of keV, or are not supported thermally. Our results represent the
first detection (with $4.4 \sigma$ significance) of this phenomenon with the SZ
effect.
