### Measuring primordial anisotropic correlators with CMB spectral distortions *[Cross-Listing]*

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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 non-vanishing $\mu$-$T$ correlation when $|\ell_1-\ell_2|=2$. 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 high signal-to-noise.