  Alternative gravity is nowadays an extremely important tool to address some
persistent observational issues, such as the dark sector of the universe. They
can also be applied to stellar astrophysics, leading to outcomes one step ahead
of those obtained through General Relativity. In the present article we test a
novel $f(R,T)$ gravity model within the physics and geometry of wormholes. The
$f(R,T)$ gravity is a reputed alternative gravity theory in which the Ricci
scalar $R$ in the Einstein-Hilbert gravitational lagrangian is replaced by a
general function of $R$ and $T$, namely $f(R,T)$, with $T$ representing the
trace of the energy-momentum tensor. We propose, for the first time in the
literature, an exponential form for the dependence of the theory on $T$. We
derive the field equations as well as the non-continuity equation and solve
those to wormhole metric and energy-momentum tensor. The importance of applying
alternative gravity to wormholes is that through these theories it might be
possible to obtain wormhole solutions satisfying the energy conditions,
departing from General Relativity well-known outcomes. In this article, we
indeed show that it is possible to obtain wormhole solutions satisfying the
energy conditions in the exponential $f(R,T)$ gravity. Naturally, there is
still a lot to do with this model, as cosmological, galactical and stellar
astrophysics applications, and the reader is strongly encouraged to do so, but,
anyhow, one can see the present outcomes as a good indicative for the theory.
