Successful models of pure gravity mediation (PGM) with radiative electroweak symmetry breaking can be expressed with as few as two free parameters, which can be taken as the gravitinomass and tan β. These models easily support a 125–126GeVHiggsmass at the expense of a scalar spectrum in the multi-TeV range and a much lighter wino as the lightest supersymmetric particle. In these models, it is a...

For control-affine systems with a proper Lyapunov function, the classical Jurdjevic–Quinn procedure (see [22]) gives a well-known and widely used method for the design of feedback controls that asymptotically stabilize the system to some invariant set. In this procedure, all controls are in general required to be activated, i.e. nonzero, at the same time. In this paper we give sufficient condit...

The nature of axion cosmology is usually said to depend on whether the Peccei–Quinn (PQ) symmetry breaks before or after inflation. The PQ symmetry itself is believed to be an accident, so there is not necessarily a symmetry during inflation at all. We explore these issues in some simple models, which provide examples of symmetry breaking before and after inflation, or in which there is no symm...

Invoking the Peccei-Quinn (PQ) solution to the strong CP problem substitutes the puzzle of why θqcd is so small with the puzzle of why the PQ symmetry is of such high quality. Cosmological and astrophysical considerations raise further puzzles. This paper explores this issues in several contexts: string theory and field theory, and theories without and with low energy supersymmetry. Among the q...

The axion solution to the strong CP problem requires an anomalous global U(1) symmetry. We show that the existence of such a symmetry is a natural consequence of an extra dimension in which a gauged U(1) is spontaneously broken on one of two branes, leaving an accidental global symmetry on the other brane. Depending on where the standard model matter lives, the resulting axion can be either the...

This essay on the nature of proof and progress in mathematics was stimulated by the article of Jaffe and Quinn, "Theoretical Mathematics: Toward a cultural synthesis of mathematics and theoretical physics". Their article raises interesting issues that mathematicians should pay more attention to, but it also perpetuates some widely held beliefs and attitudes that need to be questioned and examin...

A simple hadronic axion model is proposed in the framework of gaugemediated supersymmetry breaking. Dynamics of Peccei-Quinn symmetry breaking is governed by supersymmetry breaking effects and the Peccei-Quinn breaking scale fPQ is inversely proportional to the gravitino mass. The gravitino mass range which corresponds to the axion window fPQ ≃ 109 GeV – 1013 GeV lies in the region predicted by...

∗This work was supported by the Center for Statistics and the Social Sciences at the University of Washington with funds from the University Initiatives Funds. In addition, Quinn acknowledges research support under NSF Grant SES 01-36676. †Department of Political Science and CSSS, University of Washington, [email protected] ‡Department of Sociology, University of Washington, [email protected]...