Cross-correlation of gravitational lensing from DES Science Verification data with SPT and Planck lensing

We measure the cross-correlation between weak lensing of galaxy images and of the cosmic microwave background (CMB). The effects of gravitational lensing on different sources will be correlated if the lensing is caused by the same mass fluctuations. We use galaxy shape measurements from 139 deg$^{2}$ of the Dark Energy Survey (DES) Science Verification data and overlapping CMB lensing from the South Pole Telescope (SPT) and Planck. The DES source galaxies have a median redshift of $z_{\rm med} {\sim} 0.7$, while the CMB lensing kernel is broad and peaks at $z{\sim}2$. The resulting cross-correlation is maximally sensitive to mass fluctuations at $z{\sim}0.44$. Assuming the Planck 2015 best-fit cosmology, the amplitude of the DES$\times$SPT cross-power is found to be $A = 0.88 \pm 0.30$ and that from DES$\times$Planck to be $A = 0.86 \pm 0.39$, where $A=1$ corresponds to the theoretical prediction. These are consistent with the expected signal and correspond to significances of $2.9 \sigma$ and $2.2 \sigma$ respectively. We demonstrate that our results are robust to a number of important systematic effects including the shear measurement method, estimator choice, photometric redshift uncertainty and CMB lensing systematics. Significant intrinsic alignment of galaxy shapes would increase the cross-correlation signal inferred from the data; we calculate a value of $A = 1.08 \pm 0.36$ for DES$\times$SPT when we correct the observations with a simple IA model. With three measurements of this cross-correlation now existing in the literature, there is not yet reliable evidence for any deviation from the expected LCDM level of cross-correlation, given the size of the statistical uncertainties and the significant impact of systematic errors, particularly IAs. We provide forecasts for the expected signal-to-noise of the combination of the five-year DES survey and SPT-3G.