We construct a replica technique to perturbatively compute the odd
entanglement entropy (OEE) for bipartite mixed states in TTˉ
deformed CFT2​s. This framework is then utilized to obtain the leading order
correction to the OEE for two disjoint intervals, two adjacent intervals, and a
single interval in TTˉ deformed thermal CFT2​s in the large
central charge limit. The field theory results are subsequently reproduced in
the high temperature limit from holographic computations for the entanglement
wedge cross sections in the dual bulk finite cut off BTZ geometries. We further
show that for finite size TTˉ deformed CFT2​s at zero
temperature the corrections to the OEE are vanishing to the leading order from
both the field theory and the bulk holographic computations.Comment: 30 pages, 3 figures, 2 appendice