This work is an extension of our previous work [1] where we exploited
holography to compute the complexity characteristics of Little String Theory
(LST), a nonlocal, nongravitational field theory which flows to a local 2d CFT
in the IR under RG via an integrable irrelevant (TT) deformation. Here we look
at the more general LST obtained by UV deforming the 2d CFT by incorporating
Lorentz violating irrelevant JT and TJ deformations on top of TT deformation,
in an effort to capture the novel signatures of Lorentz violation (on top of
nonlocality) on quantum complexity. In anticipation of the fact that the dual
field theory is Lorentz violating, we compute the volume complexity in two
different Lorentz frames and the comparison is drawn between the results. It
turns out that for this system the nonlocality and Lorentz violation effects
are inextricably intertwined in the UV divergence structure of the quantum
complexity. The coefficients of the divergences carry the signature of Lorentz
boost violation. We also compute the subregion complexity which displays a
(Hagedorn) phase transition with the transition point being the same as that
for the phase transition of entanglement entropy [2]. These new results are
consistent with our previous work [1]. Null warped AdS3 is treated as an
interesting special case.
