Spread complexity is generalized to fermionic and supercoherent states, and applied to large-charge rotating strings in AdS5 x S5, yielding Krylov paths that reduce to effective SU(2)/SL(2) coherent-state complexity.
Spin chain sigma models with fermions
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The complete one-loop planar dilatation operator of N=4 supersymmetric Yang-Mills is isomorphic to the hamiltonian of an integrable PSU(2,2|4) quantum spin chain. We construct the non-linear sigma models describing the continuum limit of the SU(1|3) and SU(2|3) sectors of the complete N=4 chain. We explicitely identify the spin chain sigma model with the one for a superstring moving in AdS_5xS^5 with large angular momentum along the five-sphere.
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Spread complexity for the planar limit of holography
Spread complexity is generalized to fermionic and supercoherent states, and applied to large-charge rotating strings in AdS5 x S5, yielding Krylov paths that reduce to effective SU(2)/SL(2) coherent-state complexity.