Gauge fields as Goldstone bosons triggered by spontaneously broken supersymmetry

The emergent gauge theories are reconsidered in light of supersymmetry and an appropriate emergence conjecture is formulated. Accordingly, it might be expected that only global symmetries are fundamental symmetries of nature, whereas local symmetries and associated massless gauge fields could solely emerge due to spontaneous breaking of the underlying spacetime symmetries involved, such as relativistic invariance and supersymmetry. We further argue that this breaking, taken in the form of the nonlinear $\sigma$-model-type pattern for vector fields or superfields, puts essential restrictions on geometrical degrees of freedom of a physical field system that makes it adjust itself in such a way that its global internal symmetry $G$ turns into the local symmetry $G_{\text{loc}}$. Otherwise, a given field system could lose too many degrees of freedom, thus getting unphysical, which would make it impossible to set the required initial conditions in an appropriate Cauchy problem, or to choose self-consistent equal-time commutation relations in quantum theory. Remarkably, this emergence process may naturally be triggered by supersymmetry, as is illustrated in detail by an example of a general supersymmetric QED model which is then extended to the Standard Model and GUTs. The requirement of vacuum stability in such a class of models makes both Lorentz invariance and supersymmetry become spontaneously broken in the visible sector. As a consequence, the massless photon and other gauge bosons appear as the corresponding Goldstone and pseudo-Goldstone zero modes and special local invariance is simultaneously generated. Due to this invariance, all possible Lorentz violations turn out to be completely canceled out among themselves. However, broken supersymmetry effects related to the existence of a light pseudo-Goldstino (being essentially a photino) are still left in the theory. It typically appears in the low-energy particle spectrum as the eV-scale stable lightest supersymmetric particle or the electroweak-scale long-lived next-to-lightest supersymmetric particle, and in both cases it is accompanied by a very light gravitino that could be considered as some observational signature in favor of emergent supersymmetric theories.