String Mass Shifts

TL;DR

This paper calculates the average mass shift of closed string states at one-loop level in string theory, revealing that gravitational interactions dominate and perturbation theory remains reliable for massive states.

Contribution

It provides a novel, symmetry-based calculation of one-loop mass shifts for closed strings, including charged states, in arbitrary dimensions.

Findings

Mass shift formula: Delta M^2 = - g_s^2 M^{2+(3-D)/2}

Long-range gravitational interactions dominate corrections

Perturbation theory is reliable for massive string states

Abstract

We study closed string one-loop amplitudes in string theory, in particular the average mass shift for states at given mass and Neveu-Schwarz charges. Our analysis is based only on well-defined string amplitudes and the exploitation of symmetries and unitarity properties of the torus amplitudes. We obtain the result Delta M^2 = - g_s^2 M^(2+(3-D)/2) in D spacetime dimensions for the average closed string mas-shift (Delta M^2 = - g_s^2 (M^2-Q^2)^(1+(3-D)/4) for states with non-zero Neveu-Schwarz charges Q). An interesting picture of one-loop corrections for the string in non-supersymmetric configurations comes out: the dominant interactions responsible for these corrections are of long-range type (namely gravitational) and it appears that perturbations theory is generally reliable on the spectrum of massive string states.