An extended standard model and its Higgs geometry from the matrix model

We find a simple brane configuration in the IKKT matrix model which resembles the standard model at low energies, with a second Higgs doublet and right-handed neutrinos. The electroweak sector is realized geometrically in terms of two minimal fuzzy ellipsoids, which can be interpreted in terms of four point-branes in the extra dimensions. The electroweak Higgs connects these branes and is an indispensable part of the geometry. Fermionic would-be zero modes arise at the intersections with two larger branes, leading precisely to the correct chiral matter fields at low energy, along with right-handed neutrinos which can acquire a Majorana mass due to a Higgs singlet. The larger branes give rise to , extended by and another which are anomalous at low energies and expected to disappear. At higher energies, mirror fermions and additional fields arise, completing the full supersymmetry. The brane configuration is a solution of the model, assuming a suitable effective potential and a non-linear stabilization of the singlet Higgs. The basic results can be carried over to super YangMills on ordinary Minkowski space with sufficiently large

Spinning squashed extra dimensions and chiral gauge theory from N=4 SYM

New solutions of SU(N) N=4 SYM on R4 interpreted as spinning self-intersecting extra dimensions are discussed. Remarkably, these backgrounds lead to a low-energy sector with 3 generations of chiral fermions coupled to scalar and gauge fields, with standard Lorentz-invariant kinematics. This sector arises from zero modes localized on the rotation axes, which are oblivious to the background rotation. The remaining modes are not described by a Lorentz-invariant field theory and are mostly “heavy”, but there is one sextet of tachyonic excitations. Assuming that the latter get stabilized, e.g. by quantum effects, we argue that different rotation frequencies would induce a VEV for some of the low-energy scalar fields. We discuss configurations which may lead to a low-energy physics not far from the broken phase of the standard model

A complete survey of texture zeros in the lepton mass matrices

We perform a systematic and complete analysis of texture zeros in the lepton mass matrices and identify all viable and maximally restrictive cases of pairs ( M ℓ , M D ) and ( M ℓ , M L ), where M ℓ , M D and M L are the charged-lepton, Dirac neutrino and Majorana neutrino mass matrices, respectively. To this end, we perform a thorough analysis of textures which are equivalent through weak-basis permutations. Furthermore, we introduce numerical measures for the predictivity of textures and apply them to the viable and maximally restrictive texture zero models. It turns out that for Dirac neutrinos these models can at most predict the smallest neutrino mass and the CKM-type phase of the mixing matrix. For Majorana neutrinos most models can, in addition, predict the effective neutrino mass for neutrinoless double beta decay

Flat space (higher spin) gravity with chemical potentials

We introduce flat space spin-3 gravity in the presence of chemical potentials and discuss some applications to flat space cosmology solutions, their entropy, free energy and flat space orbifold singularity resolution. Our results include flat space Einstein gravity with chemical potentials as special case. We discover novel types of phase transitions between flat space cosmologies with spin-3 hair and show that the branch that continuously connects to spin-2 gravity becomes thermodynamically unstable for sufficiently large temperature or spin-3 chemical potential

Evolution of holographic entanglement entropy in an anisotropic system

We determine holographically 2-point correlators of gauge invariant operators with large conformal weights and entanglement entropy of strips for a time-dependent anisotropic 5-dimensional asymptotically anti-de Sitter spacetime. At the early stage of evolution where geodesics and extremal surfaces can extend beyond the apparent horizon all observables vary substantially from their thermal value, but thermalize rapidly. At late times we recover quasi-normal ringing of correlators and holographic entanglement entropy around their thermal values, as expected on general grounds. We check the behaviour of holographic entanglement entropy and correlators as function of the separation length of the strip and find agreement with the exact expressions derived in the small and large temperature limits

Lifshitz holography with isotropic scale invariance

Is it possible for an anisotropic Lifshitz critical point to actually exhibit isotropic conformal invariance? We answer this question in the affirmative by constructing a concrete holographic realization. We study three-dimensional spin-3 higher-spin gauge theory with a z = 2 Lifshitz ground state with non-trivial spin-3 background. We provide consistent boundary conditions and determine the associated asymptotic symmetry algebra. Surprisingly, we find that the algebra consists of two copies of the W 3 $${\mathcal{W}}_3$$ extended conformal algebra, which is the extended conformal algebra of an isotropic critical system. Moreover, the central charges are given by 3 ℓ/ (2 G ). We consider the possible geometric interpretation of the theory in light of the higher spin gauge invariance and remark on the implications of the asymptotic symmetry analysis

2D fuzzy anti-de Sitter space from matrix models

We study the fuzzy hyperboloids AdS 2 and dS 2 as brane solutions in matrix models. The unitary representations of SO(2 , 1) required for quantum field theory are identified, and explicit formulae for their realization in terms of fuzzy wavefunctions are given. In a second part, we study the ( A ) dS 2 brane geometry and its dynamics, as governed by a suitable matrix model. In particular, we show that trace of the energy-momentum tensor of matter induces transversal perturbations of the brane and of the Ricci scalar. This leads to a linearized form of Henneaux-Teitelboim-type gravity, illustrating the mechanism of emergent gravity in matrix models

Classification of lepton mixing matrices from finite residual symmetries

Assuming that neutrinos are Majorana particles, we perform a complete classification of all possible mixing matrices which are fully determined by residual symmetries in the charged-lepton and neutrino mass matrices. The classification is based on the assumption that the residual symmetries originate from a finite flavour symmetry group. The mathematical tools which allow us to accomplish this classification are theorems on sums of roots of unity. We find 17 sporadic cases plus one infinite series of mixing matrices associated with three-flavour mixing, all of which have already been discussed in the literature. Only the infinite series contains mixing matrices which are compatible with the data at the 3 sigma level

Calculating the chiral condensate of QCD at infinite coupling using a generalised lattice diagrammatic approach

We develop a lattice diagrammatic technique for calculating the chiral condensate of QCD at infinite coupling inspired by recent work of Tomboulis and earlier work from the 80’s. The technique involves calculating the contribution of gauge link diagrams formed from all possible combinations of a truncated number of sub-diagram types, by performing a resummation. We show how to calculate the relevant sub-diagrams, including a new technique for evaluating group integrals with arbitrary number of gauge link elements, using Young Projectors. Including up to four different diagram types we calculate the chiral condensate as a function of N f , and show that two real solutions result, which are non-zero for all integer N f . We analyse these solutions and find signs of convergence of the expansion at small N f . We should stress that a drawback of our technique is that, due to the addition of non-tree diagrams in the resummation, there are sources of error associated with miscounting and over-counting of diagrams. We discuss these sources of error in de- tail, and implement a technique to reduce over-counting of diagrams, while leaving other sources of error for future work

Double seesaw mechanism and lepton mixing

We present a general framework for models in which the lepton mixing matrix is the product of the maximal mixing matrix U ω times a matrix constrained by a well-defined ${{\mathbb{Z}}_2}$ symmetry. Our framework relies on neither supersymmetry nor non-renormalizable Lagrangians nor higher dimensions; it relies instead on the double seesaw mechanism and on the soft breaking of symmetries. The framework may be used to construct models for virtually all the lepton mixing matrices of the type mentioned above which have been proposed in the literature