  This study explores the Gaussian and the Lorentzian distributed spherically
symmetric wormhole solutions in the $f(\tau, T)$ gravity. The basic idea of the
Gaussian and Lorentzian noncommutative geometries emerges as the physically
acceptable and substantial notion in quantum physics. This idea of the
noncommutative geometries with both the Gaussian and Lorentzian distributions
becomes more striking when wormhole geometries in the modified theories of
gravity are discussed. Here we consider a linear model within $f(\tau,T)$
gravity to investigate traversable wormholes. In particular, we discuss the
possible cases for the wormhole geometries using the Gaussian and the
Lorentzian noncommutative distributions to obtain the exact shape function for
them. By incorporating the particular values of the unknown parameters
involved, we discuss different properties of the new wormhole geometries
explored here. It is noted that the involved matter violates the weak energy
condition for both the cases of the noncommutative geometries, whereas there is
a possibility for a physically viable wormhole solution. By analyzing the
equilibrium condition, it is found that the acquired solutions are stable.
Furthermore, we provide the embedded diagrams for wormhole structures under
Gaussian and Lorentzian noncommutative frameworks. Moreover, we present the
critical analysis on an anisotropic pressure under the Gaussian and the
Lorentzian distributions.
