Measuring primordial anisotropic correlators with CMB spectral distortions

We show that inflationary models with broken rotational invariance generate testable off-diagonal signatures in the correlation between the mu-type distortion and temperature fluctuations of the cosmic microwave background. More precisely, scenarios with a quadrupolar bispectrum asymmetry, usually generated by fluctuations of primordial vector fields, produce a nonvanishing mu-T correlation when vertical bar l(1) - l(2)vertical bar = 2. Since spectral distortions are sensitive to primordial fluctuations up to very small scales, a cosmic variance limited spectral distortion experiment can detect such effects with a high signal-to-noise ratio.