Vanishing of the parallel string tension at finite magnetic field

Determine whether the string tension parallel to the magnetic field, σ_parallel, vanishes at a finite value of the magnetic field in zero-temperature QCD with background magnetic fields, and if so, identify the corresponding critical field.

Background

Background magnetic fields render the static quark–antiquark potential anisotropic: the perpendicular component of the string tension increases while the parallel component decreases with B. Effective field theory arguments suggest σ_parallel→0 in the asymptotically large-B limit, but lattice results at currently accessible fields do not yet establish whether the vanishing occurs at a finite B.

Confirming a finite-B vanishing of σ_parallel would signal a qualitative change in confinement dynamics under strong fields and impact our understanding of QCD at extreme conditions.