Correlation Functions in the TsT/TTˉT{\bar T} Correspondence

We investigate the proposed holographic duality between the TsT transformation of IIB string theory on AdS$_3\times {\cal N}$ with NS-NS flux and a single-trace $T\bar{T}$ deformation of the symmetric orbifold CFT. We present a non-perturbative calculation of two-point correlation functions using string theory and demonstrate their consistency with those of the $T\bar{T}$ deformation. The two-point correlation function of the deformed theory on the plane, written in momentum space, is obtained from that of the undeformed theory by replacing $h$ with $h+2{\tilde \lambda\over w} p\bar p$, where $h$ is the spacetime conformal weight, $\tilde \lambda$ is a deformation parameter, $p$ and $\bar p$ are the momenta, and $w$ labels the twisted sectors in the deformed symmetric product. At $w=1$, the non-perturbative result satisfies the Callan-Symanzik equation for double-trace $T\bar T$ deformed CFT derived in \cite{Cardy:2019qao}. We also perform conformal perturbations on both the worldsheet CFT and the symmetric orbifold CFT as a sanity check. The perturbative and non-perturbative matching between results on the two sides provides further evidence of the conjectured TsT/$T\bar{T}$ correspondence.Comment: 35 page

Phase transitions and thermodynamics of the two-dimensional Ising model on a distorted Kagom\'{e} lattice

The two-dimensional Ising model on a distorted Kagom\'{e} lattice is studied by means of exact solutions and the tensor renormalisation group (TRG) method. The zero-field phase diagrams are obtained, where three phases such as ferromagnetic, ferrimagnetic and paramagnetic phases, along with the second-order phase transitions, have been identified. The TRG results are quite accurate and reliable in comparison to the exact solutions. In a magnetic field, the magnetization ($m$), susceptibility and specific heat are studied by the TRG algorithm, where the $m=1/3$ plateaux are observed in the magnetization curves for some couplings. The experimental data of susceptibility for the complex Co(N$_3$)$_2$(bpg)$\cdot$ DMF$_{4/3}$ are fitted with the TRG results, giving the couplings of the complex $J=22K$ and $J'=33K$