String Theory of the Regge Intercept

TL;DR

Using the Polchinski-Strominger effective string theory in covariant gauge, the authors compute the mass-squared $M^2$ of a rotating string in $D$ dimensions at large angular momentum $J$, keeping the leading Regge trajectory and including the first subleading $|J|^0$ correction. The $|J|^0$ term is shown to be universal (dependent only on $D$-dimensional Poincaré invariance and absence of extra long-range worldsheet excitations) and is obtained exactly for open strings with Neumann boundaries and for closed strings in $D\ge 5$, via semiclassical evaluation of the rotating solution plus the PS contribution. Open-string boundary renormalization is required to handle a PS anomaly at the boundary, yielding a finite $M^2$ with explicit $D$- and angular-momentum dependence; the closed-string result includes a nonzero PS term except in special limits. The work connects covariant effective string theory to Regge phenomenology, discusses relations to prior static-gauge calculations, and outlines avenues (fermionic endpoints, chiral symmetry, nonplanar effects) to bring theoretical intercepts closer to experimental hadron spectra.

Abstract

Using the Polchinski-Strominger effective string theory in covariant gauge, we compute the mass of a rotating string in D dimensions with large angular momenta J, in one or two planes, in fixed ratio, up to and including first subleading order in the large J expansion. This constitutes a first-principles calculation of the value for the order $J^0$ contribution to the mass-squared of a meson on the leading Regge trajectory in planar QCD with bosonic quarks. For open strings with Neumann boundary conditions, and for closed strings in $D\geq 5$, the order $J^0$ term in the mass-squared is exactly calculated by the semiclassical approximation. This term in the expansion is universal and independent of the details of the theory, assuming only D-dimensional Poincare invariance and the absence of other infinite-range excitations on the string worldvolume, beyond the Nambu-Goldstone bosons.