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In this paper we study string theory in the background $\mathcal{M}_3$ thatinterpolates between $AdS_3$ in the IR and linear dilaton spacetime$\mathbb{R}^{1,1}\times\mathbb{R}_\phi$ in the UV. Via holographic duality thisbackground corresponds to $\rm{CFT}_2$ deformed by a dimension $(2,2)$operator. Here we discuss the holographic Wilson loop in such a model and shedmore light in support of the non-local structure of the theory (Little StringTheory (LST)) in the UV. We also discuss quantum and thermal phase transitionsof the boundary theory.

Wilson loop in a $T\bar{T}$ like deformed $\rm{CFT}_2$