Cross-correlation of DES Y3 lensing and ACT/${\it Planck}$ thermal
  Sunyaev Zel'dovich Effect I: Measurements, systematics tests, and feedback
  model constraints
  We present a tomographic measurement of the cross-correlation between thermal
Sunyaev-Zeldovich (tSZ) maps from ${\it Planck}$ and the Atacama Cosmology
Telescope (ACT) and weak galaxy lensing shears measured during the first three
years of observations of the Dark Energy Survey (DES Y3). This correlation is
sensitive to the thermal energy in baryons over a wide redshift range, and is
therefore a powerful probe of astrophysical feedback. We detect the correlation
at a statistical significance of $21\sigma$, the highest significance to date.
We examine the tSZ maps for potential contaminants, including cosmic infrared
background (CIB) and radio sources, finding that CIB has a substantial impact
on our measurements and must be taken into account in our analysis. We use the
cross-correlation measurements to test different feedback models. In
particular, we model the tSZ using several different pressure profile models
calibrated against hydrodynamical simulations. Our analysis marginalises over
redshift uncertainties, shear calibration biases, and intrinsic alignment
effects. We also marginalise over $\Omega_{\rm m}$ and $\sigma_8$ using ${\it
Planck}$ or DES priors. We find that the data prefers the model with a low
amplitude of the pressure profile at small scales, compatible with a scenario
with strong AGN feedback and ejection of gas from the inner part of the halos.
When using a more flexible model for the shear profile, constraints are weaker,
and the data cannot discriminate between different baryonic prescriptions.
