String mass shifts

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 ΔM2=−gs2M2+3−D2 in D   space–time dimensions for the average closed string mas-shift (ΔM2=−gs2(M2−Q2)1+3−D4 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.