In this talk, we present three examples of new non-trivial vacuum structures that can occur in supersymmetric field theories, along with explicit models in which they arise. The first vacuum structure is one in which supersymmetry is broken at tree-level in a perturbative theory that also contains a supersymmetry-preserving ground state. Models realizing this structure are uniquely characterized by the fact that no flat directions appear in the classical potential, all vacua appear at finite distances in field space, and no non-perturbative physics is required for vacuum stability. The second non-trivial vacuum structure we discuss consists of large (and even infinite) towers of metastable vacua, and we show that models which give rise to such vacuum towers exhibit a rich set of instanton-induced vacuum tunneling dynamics. Finally, our third new non-trivial vacuum structure consists of an infinite number of degenerate vacua; this leads to a Bloch-wave ground state and a vacuum "band" structure. Models with such characteristics therefore experience time-dependent vacuum oscillations. Needless to say, these novel vacuum structures lead to many new potential applications for supersymmetric field theories, ranging from the cosmological-constant problem to the string landscape, supersymmetry breaking, and Z' phenomenology.
We verify a method which allows to obtain the $β$-function of supersymmetric theories regularized by higher covariant derivatives by calculating only specially modified vacuum supergraphs. With the help of this method for a general renormalizable ${\cal N}=1$ supersymmetric gauge theory a part of the three-loop $β$-function depending on the Yukawa couplings is constructed in the general $ξ$-gauge. The result is written in the form of an integral of double total derivatives with respect to the loop momenta. It is demonstrated that all gauge dependent terms cancel each other in agreement with th…
We study dynamical supersymmetry breaking in supersymmetric QCD theories for $N_f<N_c$. We consider a model with a singlet chiral superfield coupled to the infrared meson chiral superfield through a classical superpotential. We examine the vacuum structure of this model and show that in a particular limit of the parameter space with the large $N_c$ limit, it has a vacuum that dynamically breaks supersymmetry. The supersymmetric vacuum, in this limit, is being pushed to infinity.
We study the entanglement entropy of the vacuum in non-relativistic local theories with Galilean or Schrödinger symmetry. We clear some confusion in the literature on the free Schrödinger case. We find that with only positive $U(1)$ charge particles (states) and a unique zero $U(1)$ charge state (the vacuum) the entanglement entropy must vanish in that state.
We study supersymmetric inhomogeneous field theories in 1+1 dimensions which have explicit coordinate dependence. Although translation symmetry is broken, part of supersymmetries can be maintained. In this paper, we consider the simplest inhomogeneous theories with one real scalar field, which possess an unbroken supersymmetry. The energy is bounded from below by the topological charge which is not necessarily nonnegative definite. The bound is saturated if the first-order Bogomolny equation is satisfied. Non-constant static supersymmetric solutions above the vacuum involve in general a zero m…
We evaluate the quantum expectation values in non-simply connected spaces by using UV improved Green's functions proposed by Padmanabhan, Abel, and Siegel. It is found that the results from these three types of Green's functions behave similarly under changes of scales, but have minute differences. Prospects in further applications are briefly discussed.
It is known in previous literature that if a Wess-Zumino model with an R-symmetry gives a supersymmetric vacuum, the superpotential vanishes at the vacuum. In this work, we establish a formal notion of genericity, and show that if the R-symmetric superpotential has generic coefficients, the superpotential vanishes term-by-term at a supersymmetric vacuum. This result constrains the form of the superpotential which leads to a supersymmetric vacuum. It may contribute to a refined classification of R-symmetric Wess-Zumino models, and find applications in string constructions of vacua with small su…
