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In this article, we have discussed Morris and Thorne (MT) wormhole solutionsin a modified theory of gravity that admits conformal motion. Here we explorethe wormhole solutions in $f(R,\,T)$ gravity, which is a function of the Ricciscalar ($R$) and the trace of the stress-energy tensor ($T$). To study wormholegeometries, we make assumption of spherical symmetric static spacetime and theexistence of conformal Killing symmetry to get more acceptable astrophysicaloutcomes. To do this, we choose the expression of $f(R,\,T)$ as $f(R,T)= R+2\gamma T$. Here we employ the phantom energy EoS relating to radial pressureand density given by $p_r=\omega \rho$ with $\omega<-1$ to constrain our model.Following a discussion of wormhole geometry and behavior of shape function, thestudy moves on to the computation of proper radial distance, active massfunction, the nature of total gravitational energy and a discussion on theviolation of energy conditions. We have shown that the wormhole solutions existfor positive as well as negative values of the coupling constant $\gamma$. Fromour analysis we see that no wormhole solution exists for $\gamma=-4\pi,\,-\pi(3+\omega)$. All the physical parameters have been drawn byemploying the values of $\gamma$ as $\gamma=-0.3,\,-0.2,\,-0.1,\,0,\,0.1$ and$0.2$, where $\gamma=0$ corresponds to general relativity (GR) case. It isfound that for our proposed model, a realistic wormhole solutions satisfyingall the properties can be obtained.

Phantom energy supported wormhole model in $f(R,\,T)$ gravity assuming conformal motion