Dirac masses and mixings in the (geo)SM(EFT) and beyond

We report a set of exact formulae for computing Dirac masses, mixings, and CP-violation parameter(s) from 3×3 Yukawa matrices Y valid when YY† → U†YY†U under global $$ \mathrm{U}{(3)}_{Q_L} $$ U 3 Q L flavour symmetry transformations U. The results apply to the Standard Model Effective Field Theory (SMEFT) and its ‘geometric’ realization (geoSMEFT). We thereby complete, in the Dirac flavour sector, the catalogue of geoSMEFT parameters derived at all orders in the $$ \sqrt{2\left\langle {H}^{\dagger }H\right\rangle } $$ 2 H † H /Λ expansion. The formalism is basis-independent, and can be applied to models with decoupled ultraviolet flavour dynamics, as well as to models whose infrared dynamics are not minimally flavour violating. We highlight these points with explicit examples and, as a further demonstration of the formalism’s utility, we derive expressions for the renormalization group flow of quark masses, mixings, and CP-violation at all mass dimension and perturbative loop orders in the (geo)SM(EFT) and beyond.

Multiple mass hierarchies from complex fixed point collisions

A pair of complex-conjugate fixed points that lie close to the real axis generates a large mass hierarchy in the real renormalization group flow that passes in between them. We show that pairs of complex fixed points that are close to the real axis and to one another generate multiple hierarchies, some of which can be parametrically enhanced. We illustrate this effect at weak coupling with field-theory examples, and at strong coupling using holography. We also construct complex flows between complex fixed points, including flows that violate the c-theorem.

3d large $N$ vector models at the boundary

We consider a 4d scalar field coupled to large NN free or critical O(N)O(N) vector models, either bosonic or fermionic, on a 3d boundary. We compute the \betaβ function of the classically marginal bulk/boundary interaction at the first non-trivial order in the large NN expansion and exactly in the coupling. Starting with the free (critical) vector model at weak coupling, we find a fixed point at infinite coupling in which the boundary theory is the critical (free) vector model and the bulk decouples. We show that a strong/weak duality relates one description of the renormalization group flow to another one in which the free and the critical vector models are exchanged. We then consider the theory with an additional Maxwell field in the bulk, which also gives decoupling limits with gauged vector models on the boundary.

The cubic fixed point at large N

By considering the renormalization group flow between N coupled Ising models in the UV and the cubic fixed point in the IR, we study the large N behavior of the cubic fixed points in three dimensions. We derive a diagrammatic expansion for the 1/N corrections to correlation functions. Leading large N corrections to conformal dimensions at the cubic fixed point are then evaluated using numeric conformal bootstrap data for the 3d Ising model.

Free energy and defect C-theorem in free fermion

We describe a p-dimensional conformal defect of a free Dirac fermion on a d-dimensional flat space as boundary conditions on a conformally equivalent space ℍp+1×$$ \mathbbm{S} $$ S d−p−1. We classify allowed boundary conditions and find that the Dirichlet type of boundary conditions always exists while the Neumann type of boundary condition exists only for a two-codimensional defect. For the two-codimensional defect, a double trace deformation triggers a renormalization group flow from the Neumann boundary condition to the Dirichlet boundary condition, and the free energy at UV fixed point is always larger than that at IR fixed point. This provides us with further support of a conjectured C-theorem in DCFT.

Generalized global symmetries of T[M] theories. Part I

We study reductions of 6d theories on a d-dimensional manifold Md, focusing on the interplay between symmetries, anomalies, and dynamics of the resulting (6 −d)-dimensional theory T[Md]. We refine and generalize the notion of “polarization” to polarization on Md, which serves to fix the spectrum of local and extended operators in T[Md]. Another important feature of theories T[Md] is that they often possess higher-group symmetries, such as 2-group and 3-group symmetries. We study the origin of such symmetries as well as physical implications including symmetry breaking and symmetry enhancement in the renormalization group flow. To better probe the IR physics, we also investigate the ’t Hooft anomaly of 5d Chern-Simons matter theories. The present paper focuses on developing the general framework as well as the special case of d = 0 and 1, while an upcoming paper will discuss the case of d = 2, 3 and 4.