Search results for "Lower dimension"
showing 4 items of 4 documents
The 1-loop effective potential for the Standard Model in curved spacetime
2018
The renormalisation group improved Standard Model effective potential in an arbitrary curved spacetime is computed to one loop order in perturbation theory. The loop corrections are computed in the ultraviolet limit, which makes them independent of the choice of the vacuum state and allows the derivation of the complete set of $\beta$-functions. The potential depends on the spacetime curvature through the direct non-minimal Higgs-curvature coupling, curvature contributions to the loop diagrams, and through the curvature dependence of the renormalisation scale. Together, these lead to significant curvature dependence, which needs to be taken into account in cosmological applications, which i…
Measures with predetermined regularity and inhomogeneous self-similar sets
2016
We show that if $X$ is a uniformly perfect complete metric space satisfying the finite doubling property, then there exists a fully supported measure with lower regularity dimension as close to the lower dimension of $X$ as we wish. Furthermore, we show that, under the condensation open set condition, the lower dimension of an inhomogeneous self-similar set $E_C$ coincides with the lower dimension of the condensation set $C$, while the Assouad dimension of $E_C$ is the maximum of the Assouad dimensions of the corresponding self-similar set $E$ and the condensation set $C$. If the Assouad dimension of $C$ is strictly smaller than the Assouad dimension of $E$, then the upper regularity dimens…
Monopoles and dualities in 3d N=2 quivers
2021
Seiberg-like dualities in 2+1d quiver gauge theories with 4 supercharges are investigated. We consider quivers made of various combinations of classical gauge groups U(N), Sp(N), SO(N) and SU(N). Our main focus is the mapping of the supersymmetric monopole operators across the dual theories. There is a simple general rule that encodes the mapping of the monopoles upon dualizing a single node. This rule dictates the mapping of all the monopoles which are not dressed by baryonic operators. We also study more general situations involving baryons and baryon-monopoles, focussing on three examples: SU−Sp, SO−SO and SO−Sp quivers.
Assouad Type Dimensions in Geometric Analysis
2021
We consider applications of the dual pair of the (upper) Assouad dimension and the lower (Assouad) dimension in analysis. We relate these notions to other dimensional conditions such as a Hausdorff content density condition and an integrability condition for the distance function. The latter condition leads to a characterization of the Muckenhoupt Ap properties of distance functions in terms of the (upper) Assouad dimension. It is also possible to give natural formulations for the validity of Hardy–Sobolev inequalities using these dual Assouad dimensions, and this helps to understand the previously observed dual nature of certain cases of these inequalities. peerReviewed