tokens: Zanazzi Lai 2018 ). If the initial inclination angle of the disc is small, the result of the evolution is that the disc tends to be coplanar with the binary star. If the initial inclination angle of the disc is large (i.e. >40°; Martin Lubow 2017 ) and the eccentricity of the binary star is non-negligible, then the disc will evolve into a polar orbit. The presence of high-inclination discs indicates that high-inclination CBPs might exist. However, the above conclusions are based on the evolution of the isolated CBD systems themselves. Besides, they can only evolve to high-inclination orbits in specific initial configurations, such as a high initial inclination and a large eccentricity for the binary. Other mechanisms are still needed to explain why the CBD has a large inclination initially. It is worth noting that the semimajor axes of binaries with high-inclination discs found already are relatively large (several tens of au), while the discs around close binaries are nearly coplanar (Kennedy et al. 2012 ; Czekala et al. 2019 ). For the Kepler CBPs, the semimajor axes of their host binaries are small, about 0.1–0.2 au. One possibility is that the discs around well-spaced binaries are susceptible to the surrounding environment, such as th close encounters with fly-by stars. It is generally believed that most stars, and therefore most planetary systems, were born in clusters or associations (Clarke, Bonnell Hillenbrand 2000 ; Lada Lada 2003 ; Pfalzner 2013 ; Hao, Kouwenhoven Spurzem 2013 ; Cai et al. 2017 ). Some open clusters later dissolved, forming the current field stars. A notable example is that our own Solar system may have formed in an open cluster. The chemical composition of objects in the Solar system, along with the orbital elements of Sedna, suggest that the Sun formed in a cluster with roughly 10 3 –10 4 stars (Adams 2010 ). Other work even suggests that the Sun was born in a massive cluster (10 4 –10 5 stars) because a cluster of several thousand stars is much too small to produce a nearby massive supernova (Dukes Krumholz 2012 ). Malmberg, Davies Heggie ( 2011 ) considered the effect of a close encounter between stars on the planetary systems in a single star system. They found that the fly-by of a star is one of the possible mechanisms for explaining the generally high eccentricity of exoplanes (mainly discovered by radial velocity methods). It is interesting to ask how the cluster environment affects CBPs. In fact, the first CBP discovered, PSR B1620–26, is located in a globular cluster (Sigurdsson et al. 2003 ). According to the theory of star formation, it is impossible to form a close binary directly (Moe Kratter 2018 ). One of the explanations for this is that they are formed by interaction with other stars (Martin, Mazeh Fabrycky 2015 ; Hamers, Perets Portegies Zwart 2016 ; Moe Kratter 2018 ), which means that they were in a star-dense environment previously. A cluster provides such a possibility. If a CBP was born in an
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