A systematic construction of the physical spectrum in string theory is still missing. In the Pure Spinor String there’s been progress in the construction of massless states using the BRST charge. For massive states the task is daunting, even in flat space. A simpler requirement for physical operators in string theory is to have vanishing worldsheet anomalous dimension. In this talk we derive the rules for a systematic computation of the worldsheet anomalous dimension of any operator on a $AdS_5\times S^5$ background. Also, another approach to construct the spectrum of physical states is discussed using a supertwistor space formulation.