  Among the several modified/extended gravity paradigms, the concept of
antisymmetric connections leading to space-time torsion can be traced back to
Cartan. More recently, developments in string theory have suggested the
existence of a rank-2 self-interacting tensor field called the Kalb-Ramond
field with similar outcomes, the field strength of which can support analytic
wormhole-like solutions. However, detailed analyses of the physical properties
of interest of such solutions are lacking. In this study, we comprehensively
probe the properties of traversable Morris-Thorne like wormhole solutions
sourced by the Kalb-Ramond field strength in both General Relativity (GR) and
$f(R)$ and $f(R,T)$ modified gravity. We also analyze the coupling of the field
strength in GR via a novel non-minimal interaction term in the action. Using
suitable parametric constraints in all cases, we evaluate wormhole shape
functions, numerically analyze the energy conditions near the throat, check the
stability using the generalized Tolman-Oppenheimer-Volkov equation, and
demonstrate the possibility of minimum exotic matter by estimating the volume
integral quantifier. Our results show the existence of stable wormhole
solutions in GR and a simple $f(R,T)$ gravity model, and unstable ones in a
power-law type $f(R)$ gravity model.

General Relativity and Quantum Cosmology