The superworld (Q2755519)

The paper is based on a talk of the author describing for a broad audience some aspects of the world of supersymmetric phenomena. He first reviews the main features of the standard model in particle physics: its compatibility with special relativity as local quantum field theory, the presence of local \(SU(3)\times SU(2)\times U(1)\) gauge symmetry that acts on gauge particles and matter particles, and the set of parameters (masses and structure constants). Despite its unprecedented success as a theory of particle physics in excellent agreement with experiment, there are several questions posed by the standard model, which seem out of reach at present: the problem of integrating gravity (general relativity), a justification of the energy scale and parameters, and the question of whether new physical phenomena lie in the energy range in between the level currently accessible to experiment (a few hundred GeV) and the Planck mass scale of \(10^{19}\) GeV.NEWLINENEWLINENEWLINESupersymmetry is a symmetry interchanges bosons and fermions. It is formally treated by adding anticommuting coordinates to the usual space-time coordinates. The appearance of supersymmetry, that some expect to find in the TeV energy range, produces important effects of cancellation between boson and fermion contributions in loop diagrams, which makes it possible to analyze supersymmetric theories exactly.NEWLINENEWLINENEWLINEReasons why physicists expect all superpartners of particles in the standard model to have masses not greater than a few TeV lie in the resulting cancellations in loop diagrams between bosons and fermions, which solves a technical issue related to diagrammatic calculations. This, together with ideas from gauge unification, and possibly the relevance in dark matter questions, lead to the widespread expectation that supersymmetry will be detectable at low enough energy (in the TeV range).NEWLINENEWLINENEWLINEAn important conceptual advantage of supersymmetric quantum field theories is that they can be analyzed exactly, due to the high number of constraints imposed on the system by the supersymmetry condition, which result in holomorphicity conditions. These theories exhibit an infinite family of inequivalent vacua. This helps in the study of solutions via asymptotic methods, while the holomorphicity condition helps in showing uniqueness of solutions.NEWLINENEWLINENEWLINESupersymmetry also plays a crucial role in unifying the different versions of string theory. String theory also shares the property of having many inequivalent vacua, and their supersymmetric compactifications are connected, which makes it possible to extrapolate from the boundary to a unique underlying M-theory.NEWLINENEWLINEFor the entire collection see [Zbl 0958.00052].