Clifford-based spectral action and renormalization group analysis of the gauge couplings

The Spectral Action Principle in noncommutative geometry derives the actions of the Standard Model and General Relativity (along with several other gravitational terms) by reconciling them in a geometric setting, and hence offers an explanation for their common origin. However, one of the requirements in the minimal formalism, unification of the gauge coupling constants, is not satisfied, since the basic construction does not introduce anything new that can change the renormalization group (RG) running of the Standard Model. On the other hand, it has been recently argued that incorporating structure of the Clifford algebra into the finite part of the spectral triple, the main object that encodes the complete information of a noncommutative space, gives rise to five additional scalar fields in the basic framework. We investigate whether these scalars can help to achieve unification. We perform a RG analysis at the one-loop level, allowing possible mass values of these scalars to float from the electroweak scale to the putative unification scale. We show that out of twenty configurations of mass hierarchy in total, there does not exist even a single case that can lead to unification. In consequence, we confirm that the spectral action formalism requires a model-construction scheme beyond the (modified) minimal framework.Comment: 20 pages, 1 figure, 1 table of results; matches the published versio

Dynamical Four-Form Fields

We present an example of a gauge-invariant Lagrangian that contains four derivatives and describes one massive, non-ghostlike, degree of freedom.Comment: 5 page

Gauge non-invariance as tests of emergent gauge symmetry

We motivate the concept of emergent gauge symmetry and discuss ways that this concept can be tested. The key idea is that if a symmetry is emergent, one should look for small violations of this symmetry because the underlying fundamental theory does not contain the symmetry. We describe our recent work implementing this idea in the gravity sector. We also describe the reasons why violations of gauge symmetry may well be linked to violations of Lorentz invariance.Comment: 5 pages, Invited talk presented at the Fifth Meeting on CPT and Lorentz Symmetry, Bloomington, Indiana, June 28-July 2, 201

BB-decay anomalies and scalar leptoquarks in unified Pati-Salam models from noncommutative geometry

Motivated by possible scalar-leptoquark explanations of the recently reported $B$-decay anomalies, we investigate whether the required leptoquarks can be accommodated within models based on noncommutative geometry (NCG). The models considered have the gauge structure of Pati-Salam models, $SU(4)\times SU(2)_L\times SU(2)_R$, with gauge coupling unification at a single scale. In one of the models, we find a unique scalar leptoquark with quantum numbers $(3,1,-\frac{1}{3})_{321}$, originating from a complex multiplet $(6,1,1)_{422}$, which can potentially explain the $B$-decay anomalies if its mass is on the order of a few TeV. The unification of couplings can be realized with the inclusion of a single step of intermediate symmetry breaking. The scalar leptoquark under consideration does not contribute to proton decay due to the absence of diquark couplings, as dictated by the underlying noncommutative geometry.Comment: 40 pages, 5 figures; references added, typos corrected, minor clarifications made. Published version in JHE