Debris disks are usually detected through the infrared excess over the photospheric level of their host star. The most favorable stars for disk detection are those with spectral types between A and K, while the statistics for debris disks detected around low-mass M-type stars is very low, either because they are rare or because they are more difficult to detect. Terrestrial planets, on the other hand, may be common around M-type stars. Here, we report on the discovery of an extended (likely) debris disk around the M-dwarf GSC 07396-00759. The star is a wide companion of the close accreting binary V4046 Sgr. The system probably is a member of the $beta$ Pictoris Moving Group. We resolve the disk in scattered light, exploiting high-contrast, high-resolution imagery with the two near-infrared subsystems of the VLT/SPHERE instrument, operating in the YJ bands and the H2H3 doublet. The disk is clearly detected up to 1.5 ($sim110$ au) from the star and appears as a ring, with an inclination $isim83$ degree, and a peak density position at $sim 70$ au. The spatial extension of the disk suggests that the dust dynamics is affected by a strong stellar wind, showing similarities with the AU Mic system that has also been resolved with SPHERE. The images show faint asymmetric structures at the widest separation in the northwest side. We also set an upper limit for the presence of giant planets to $2 M_J$. Finally, we note that the 2 resolved disks around M-type stars of 30 such stars observed with SPHERE are viewed close to edge-on, suggesting that a significant population of debris disks around M dwarfs could remain undetected because of an unfavorable orientation.
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