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We present a multi-wavelength analysis of the galaxy cluster A1668, performedby means of new EVLA and Chandra observations and archival H$\alpha$ data. Theradio images exhibit a small central source ($\sim$14 kpc at 1.4 GHz) withL$_{\text{1.4 GHz}}$ $\sim$6 $\cdot$ 10$^{23}$ W Hz$^{-1}$. The mean spectralindex between 1.4 GHz and 5 GHz is $\sim$ -1, consistent with the usual indicesfound in BCGs. The cooling region extends for 40 kpc, with bolometric X-rayluminosity L$_{\text{cool}} = 1.9\pm 0.1 \cdot$ 10$^{43}$ erg s$^{-1}$. Wedetect an offset of $\sim$ 6 kpc between the cluster BCG and the X-ray peak,and another offset of $\sim$ 7.6 kpc between the H$\alpha$ and the X-ray peaks.We discuss possible causes for these offsets, which suggest that the coolestgas is not condensing directly from the lowest-entropy gas. In particular, weargue that the cool ICM was drawn out from the core by sloshing, whereas theH$\alpha$ filaments were pushed aside from the expanding radio galaxy lobes. Wedetect two putative X-ray cavities, spatially associated to the west radio lobe(cavity A) and to the east radio lobe (cavity B). The cavity power and age ofthe system are P$_{\text{cav}} \sim$ 9 $\times$10$^{42}$ erg s$^{-1}$ andt$_{\text{age}} \sim$5.2 Myr, respectively. Evaluating the position of A1668 inthe cooling luminosity-cavity power parameter space, we find that the AGNenergy injection is currently consistent within the scatter of therelationship, suggesting that offset cooling is likely not breaking the AGNfeedback cycle.

A first Chandra view of the cool core cluster A1668: offset cooling and AGN feedback cycle