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Abstract Theories with compact extra dimensions can exhibit a vacuum instability known as a bubble of nothing. These decay modes can be obstructed if the internal manifold is stabilized by fluxes, or if it carries Wilson lines for background gauge fields, or if the instanton is incompatible with the spin structure. In each of these cases the decay can proceed by adding dynamical charged membranes or gauge fields. We give a general, bottom-up procedure for constructing approximate bubble of nothing solutions in models with internal spheres stabilized by flux and study the influence of the brane tension on the tunneling exponent, finding two branches of solutions that merge at a minimal superextremal value of the tension. In the case of Wilson operators and incompatible fermions, the relevant bubble is shown to be the Euclidean Reissner-Nordstrom black hole, and the ordinary decay exponent is modified by 1/g 2 effects. We examine the Dirac operator on this background and comment on the relevance for models of supergravity with gauged R-symmetry.

Abstract In this work we present a new class of N $$ \mathcal{N} $$ = 1 supersymmetric confining gauge theories, with strikingly simple infrared theories that descend from intricate interconnected networks of product gauge groups. A diagram of the gauge groups and the charged matter content of the ultraviolet theory has the structure of a triangular lattice, with SU(N) or SU(3N) gauge groups at each of the vertices, connected by bifundamental chiral superfields. This structure admits a U(1) R conserving superpotential with marginal (trilinear) operators. With the introduction of this superpotential, the SU(3N) and SU(N) gauge groups confine: in the far infrared limit of the supersymmetric theory, the relevant degrees of freedom are gauge invariant “mesons” and “baryons.” In this paper we show how the properties of the infrared degrees of freedom depend on the topology and shape of the moose/quiver “lattice” of the original gauge theory. Between the local structure of the moose lattice at higher energies, and the boundary dependence that emerges in the infrared, the 4d moose lattice theory reproduces features of a 6d spacetime with two compact dimensions. We investigate various deformations of the theory, and propose some phenomenological applications for BSM models.

Abstract Bubbles of nothing are a class of vacuum decay processes present in some theories with compactified extra dimensions. We investigate the existence and properties of bubbles of nothing in models where the scalar pseudomoduli controlling the size of the extra dimensions are stabilized at positive vacuum energy, which is a necessary feature of any realistic model. We map the construction of bubbles of nothing to a four-dimensional Coleman-De Luccia problem and establish necessary conditions on the asymptotic behavior of the scalar potential for the existence of suitable solutions. We perform detailed analyses in the context of five-dimensional theories with metastable dS4 × S 1 vacua, using analytic approximations and numerical methods to calculate the decay rate. We find that bubbles of nothing sometimes exist in potentials with no ordinary Coleman-De Luccia decay process, and that in the examples we study, when both processes exist, the bubble of nothing decay rate is typically faster. Our methods can be generalized to other stabilizing potentials and internal manifolds.

Abstract The strong CP problem is a compelling motivation for physics beyond the Standard Model. The most popular solutions invoke a global U(1)PQ symmetry, but are challenged by quantum gravitational corrections which are thought to be incompatible with global symmetries, arguing that realistic theories contain additional structure. We explore a construction in which the U(1)PQ symmetry is protected to arbitrary order by virtue of a supersymmetric, confining SU(N) L × SU(N) × SU(N) R × U(1) X product gauge group, achieving θ ¯ $$ \left|\overline{\uptheta}\right| $$ < 10−11 for an SU(5) model with f a ≲ 3 × 1011 GeV. This construction leads to low energy predictions such as a U(1) X gauge symmetry, and for X = B − L engineers a naturally O $$ \mathcal{O} $$ (TeV) value for the μ parameter of the MSSM.

Abstract A global U(1)PQ symmetry is protected from gravitational effects in the s-confining SU(N) k product group theory with A+4Q+NQ¯ $$ A + 4Q+N\overline{Q} $$ matter. If the SU(4) family symmetry is gauged and an appropriate tree-level superpotential is added, then the dynamically generated superpotential spontaneously breaks SU(4) × U(1)PQ → SU(3) c and produces a QCD axion. Small values of the CP -violating θ parameter are then possible without any fine-tuning, as long as the product group is suitably large. By introducing a second copy of the s-confining SU(N) product group also coupled to the gauged SU(4), we find that values as small as N = 7 are consistent with θ¯

Abstract We propose a new set of s-confining theories with product gauge groups and no tree-level superpotential, based on a model with one antisymmetric matter field and four flavors of quarks. For each product group we find a set of gauge-invariant operators which satisfy the ’t Hooft anomaly matching conditions, and we identify the dynamically generated superpotential which reproduces the classical constraints between operators. Several of these product gauge theories confine without breaking chiral symmetry, even in cases where the classical moduli space is quantum-modified. These results may be useful for composite model building, particularly in cases where small operators of the form Q Q ¯ $$ \left(Q\overline{Q}\right) $$ are absent, or for theories with multiple natural energy scales, and may provide new ways to break supersymmetry dynamically.