Exponential suppression of the cosmological constant in nonsupersymmetric string vacua at two loops and beyond

Abstract

Two independent criteria are presented that together guarantee exponential suppression of the two-loop cosmological constant in non-supersymmetric heterotic strings. They are derived by performing calculations in both the full string theory and in its effective field theory, and come respectively from contributions that involve only physical untwisted states, and contributions that include orbifold twisted states. The criteria depend purely on the spectrum and charges, so a model that satisfies them will do so with no fine-tuning. An additional consistency condition (emerging from the so-called separating degeneration limit of the two-loop diagram) is that the one-loop cosmological constant must also be suppressed, by Bose-Fermi degeneracy in the massless spectrum. We comment on the effects of the residual exponentially suppressed one-loop dilaton tadpole, with the conclusion that the remaining instability would be under perturbative control in a generic phenomenological construction. We remark that theories of this kind, that have continued exponential suppression to higher orders, can form the basis for a string implementation of the "naturalness without supersymmetry" idea.

Non-supersymmetric D-branes with vanishing cylinder amplitudes in asymmetric orbifolds

“…Furthermore, in a given non-BPS D-brane background, the contributions to the closed-string vacuum amplitude would come only from the diagrams with the external legs sourced by that non-BPS D-brane. The analysis of the loops thus would be much simpler than the case of the bulk SUSY-breaking [1,3,9,20], to control the almost vanishing cosmological constant. It would also be challenging to substantiate the scenario [4], which is based on the analysis on the heterotic dual side and mentioned in the introduction, that the non-BPS D-branes condensate to produce the non-perturbative mismatch of the spectrum.…”

“…Studies of non-SUSY vacua in heterotic string theory have also been presented e.g. in [13][14][15][16][17][18][19][20].…”

GUT precursors and entwined SUSY: The phenomenology of stable nonsupersymmetric strings

“…Such conditions were derived in Ref. [62], and interestingly the condition for the suppression of a generic two-loop cosmological constant is that the sum over the one-loop scalar squared masses also be exponentially suppressed. This would then suggest a possible connection between the exponential suppression of scalar squared masses and higher-loop stability.…”

Supersymmetry breaking in heterotic strings and the decompactification problem

“…More recently, in the context of string phenomenology, there has been an increased interest in nonsupersymmetric string constructions [16,17,18,35,19,20,21,22,23,24,25,26,27,28,29,30] and, in particular, there has been considerable progress in understanding radiative corrections to gauge and gravitational couplings in such setups. Part of this progress was possible thanks to the development of new mathematical techniques for studying string loop amplitudes [31,32,33,34,35,36].…”