Non-renormalization of mass of some non-supersymmetric string states

Abstract

It is argued that the quantum correction to the mass of some very massive, nonsupersymmetric states vanishes in inverse proportion to their tree-level mass to all orders in string loops. This approximate nonrenormalization can explain the agreement between the perturbative degeneracy of these states and the Sen entropy of the associated black holes.

Duality and Decay of MacroscopicFStrings

“…Most massive closed strings are unstable and decay [10][11][12][13][14][15] [16,17], typical decay rates being (when massive radiation is negligible),…”

“…There are also more stable near-BPS trajectories (see e.g. [13]) and approximate non-renormalisation theorems [15]. Stable BPS states in turn provide a window into non-perturbative physics [18] [19][20][21].…”

“…Traditionally, these are described in a mass eigenstate basis, and calculations almost exclusively [10][11][12][13][14][15][16][17] focus on leading Regge trajectory states which do not exhibit generic features (such as non-degenerate cusps [27]). Although physical vertex operators for arbitrary mass eigenstates are known [9], they are not a natural basis for highly excited strings as the resulting amplitudes generically become unwieldy.…”

“…Decay rates may be extracted from the imaginary part of two-point amplitudes [10][11][12][13][14][15] [32,33,35]. When strings in the loops go onshell, they can appear in final states.…”

“…When strings in the loops go onshell, they can appear in final states. In the usual approach [10][11][12][13][14][15], dependence on the loop momenta is not manifest, and so one does not have a handle on the frequency and isotropy of the emitted radiation. We bypass this obstacle by considering instead the fixed (A-cycle) loop momentum amplitude [32], M(P), defined (at genus-…”