Integrability treatment of AdS/CFT orbifolds

We elaborate on the treatment of orbifolds of type IIB string theory on A d S 5 × S 5 and their dual gauge theories with integrability techniques. The implementation of orbifolds via twisted spin-chains, thermodynamic Bethe ansatz equations with chemical potentials and Y - and T -systems with modified asymptotics is confronted with twisted boundary conditions of the string sigma-model. This allows us to consistently twist the quantum spectral curve, which is believed to bridge the two sides of the AdS/CFT duality. We discuss Abelian orbifolds of P S U ( 2 , 2 | 4 ) and treat the special cases of supersymmetric Z 2 -orbifolds and type 0B string theory on A d S 5 × S 5 as primary examples. This opens a pathway to probe the validity of the duality and to study the long-standing question of tachyon stabilisation in non-supersymmetric AdS/CFT. We comment on the current understanding of this issue and point out the next steps in this challenge.