An assembly for a gas turbine, the assembly comprising; a turbine including an array of turbine blades mounted on a rotor, a gas turbine casing radially outboard of the turbine; an annular seal segment assembly arranged radially inboard of the gas turbine casing and surrounding the turbine adjacent to the turbine blades; an abradable coating on an inboard surface of each seal segment of the seal segment assembly for contact with the tips of the turbine blades when in use; a plurality of rows of coolant ducts extending from an outboard surface of a respective seal segment, through the seal segment and the abradable coating, for carrying a coolant towards the blade tips; and a plurality of grooves formed in the inboard surface of the abradable coating, each coolant duct opening into one of the plurality of grooves, the grooves extending predominantly in a circumferential direction around the annular seal segment and wherein a mouth of each groove opening towards the turbine blades is no narrower than an inner end of the groove which is furthest from the blade, wherein at least one of the grooves terminates in end walls within a perimeter of the abradable coating of the seal segment and at least one end wall of a groove is radiused to provide a smooth, concave shape to the groove in cross-section through an axis of the groove, to turn entrained air inwards towards the blade tips. a turbine including an array of turbine blades mounted on a rotor, a gas turbine casing radially outboard of the turbine; an annular seal segment assembly arranged radially inboard of the gas turbine casing and surrounding the turbine adjacent to the turbine blades; an abradable coating on an inboard surface of each seal segment of the seal segment assembly for contact with the tips of the turbine blades when in use; a plurality of rows of coolant ducts extending from an outboard surface of a respective seal segment, through the seal segment and the abradable coating, for carrying a coolant towards the blade tips; and an annular seal segment assembly arranged radially inboard of the gas turbine casing and surrounding the turbine adjacent to the turbine blades; an abradable coating on an inboard surface of each seal segment of the seal segment assembly for contact with the tips of the turbine blades when in use; a plurality of rows of coolant ducts extending from an outboard surface of a respective seal segment, through the seal segment and the abradable coating, for carrying a coolant towards the blade tips; and a plurality of grooves formed in the inboard surface of the abradable coating, each coolant duct opening into one of the plurality of grooves, the grooves extending predominantly in a circumferential direction around the annular seal segment and wherein a mouth of each groove opening towards the turbine blades is no narrower than an inner end of the groove which is furthest from the blade, wherein at least one of the grooves terminates in end walls within a perimeter of the abradable coating of the seal segment and at least one end wall of a groove is radiused to provide a smooth, concave shape to the groove in cross-section through an axis of the groove, to turn entrained air inwards towards the blade tips.