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The exquisitely measured maps of fluctuations in the Cosmic MicrowaveBackground (CMB) present the possibility to test the principle of StatisticalIsotropy (SI) of the Universe through systematic observable measures fornon-Statistical Isotropy (nSI) features in the data. Recent measurements of theCMB temperature field provide tantalizing evidence of the deviation from SI. Asystematic approach based on strong mathematical formulation allows any nSIfeature to be traced to known physical effects or observational artefacts.Unexplained nSI features could have immense cosmological ramifications for thestandard model of cosmology. BipoSH (Bipolar Spherical Harmonics) provides ageneral formalism for quantifying the departure from statistical isotropy for afield on a 2D sphere. We adopt a known reduction of the BipoSH functions,dubbed Minimal Harmonics (Manakov et al. 1996). We demonstrate that thisreduction technique of BipoSH leads to a new generalized set of isotropicangular correlation functions (mBipoSH) that are observable quantifications ofnSI features in a sky map. We show that any nSI feature in the CMB map capturedby BipoSH at the bipolar multiple $L$ with projection $M$ can be studied by$(L+1)$ mBipoSH angular correlation functions in case of even parity and by $L$functions in case of odd parity. We present in this letter a novel observablequantification of deviation from statistical isotropy in terms of generalizedangular correlation functions that are compact and complementary to the BipoSHspectra that generalize angular power spectrum CMB fluctuations.

Capturing Statistical Isotropy violation with generalized Isotropic Angular Correlation Functions of CMB Anisotropy