An arrangement for a gas turbine engine includes a combustor for producing a working medium by combustion of a mixture of fuel and an oxidant, a turbine section comprising a stationary vane carrier on which a first row of stationary vanes is arranged, and a transition duct for leading the working medium from the combustor to the turbine section. The transition duct has a forward end that adjoins the combustor and an aft end that adjoins the stationary vane carrier. The transition duct has a transition duct axis extending from the forward end to the aft end along a straight line. The transition duct axis is normal to a vane axis of a stationary vane in the first row of stationary vanes.