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A recent photometric survey in the NGC~3766 cluster led to the detection ofstars presenting an unexpected variability. They lie in a region of theHertzsprung-Russell (HR) diagram where no pulsation are theoretically expected,in between the $\delta$ Scuti and slowly pulsating B (SPB) star instabilitydomains. Their variability periods, between $\sim$0.1--0.7~d, are outside theexpected domains of these well-known pulsators. The NCG~3766 cluster is knownto host fast rotating stars. Rotation can significantly affect the pulsationproperties of stars and alter their apparent luminosity through gravitydarkening. Therefore we inspect if the new variable stars could correspond tofast rotating SPB stars. We carry out instability and visibility analysis ofSPB pulsation modes within the frame of the traditional approximation. Theeffects of gravity darkening on typical SPB models are next studied. We findthat at the red border of the SPB instability strip, prograde sectoral (PS)modes are preferentially excited, with periods shifted in the 0.2--0.5~d rangedue to the Coriolis effect. These modes are best seen when the star is seenequator-on. For such inclinations, low-mass SPB models can appear fainter dueto gravity darkening and as if they were located between the $\delta$~Scuti andSPB instability strips.

Are the stars of a new class of variability detected in NGC~3766 fast rotating SPB stars?