The exact decomposition of gauge variables in lattice Yang–Mills theory

In this Letter, we consider lattice versions of the decomposition of the Yang–Mills field a la Cho–Faddeev–Niemi, which was extended by Kondo, Shinohara and Murakami in the continuum formulation. For the SU(N)$\mathit{SU}(N)$ gauge group, we propose a set of defining equations for specifying the decomposition of the gauge link variable and solve them exactly without using the ansatz adopted in the previous studies for SU(2)$\mathit{SU}(2)$ and SU(3)$\mathit{SU}(3)$. As a result, we obtain the general form of the decomposition for SU(N)$\mathit{SU}(N)$ gauge link variables and confirm the previous results obtained for SU(2)$\mathit{SU}(2)$ and SU(3)$\mathit{SU}(3)$.     

Six-dimensional Yang black holes in dilaton gravity

We study the six-dimensional dilaton gravity Yang black holes of Bergshoeff, Gibbons and Townsend, which carry (1,−1)$(1,-1)$ charge in SU(2)×SU(2)$\mathit{SU}(2)\times \mathit{SU}(2)$ gauge group. We find what values of the asymptotic parameters (mass and scalar charge) lead to a regular horizon, and show that there are no regular solutions with an extremal horizon.     

The 't Hooft–Polyakov monopole in the presence of a 't Hooft operator

We present explicit BPS field configurations representing one non-Abelian monopole with one minimal weight 't Hooft operator insertion. We explore the SO(3)$\mathit{SO}(3)$ and SU(2)$\mathit{SU}(2)$ gauge groups. In the case of SU(2)$\mathit{SU}(2)$ gauge group the minimal 't Hooft operator can be completely screened by the monopole. If the gauge group is SO(3)$\mathit{SO}(3)$, however, such screening is impossible. In the latter case we observe a different effect of the gauge symmetry enhancement in the vicinity of the 't Hooft operator.     

Modifications to the properties of the Higgs boson

We explore the impact of new SU(3)×SU(2)×U(1)$\mathit{SU}(3)\times \mathit{SU}(2)\times U(1)$ invariant interactions characterized by a scale of order a TeV on Higgs boson properties. The Higgs production rate and branching ratios can be very different from their standard model values. We also discuss the possibility that these new interactions contribute to acceptable unification of the gauge couplings.     

Zero modes for the boundary giant magnons

We study the fermion zero-mode dynamics for open strings ending on the giant graviton branes. For the open string ending on the Z=0$Z=0$ brane, the quantization of the fermion zero-modes of boundary giant magnons reproduces the 256 states of the boundary degrees with the precise realization of the SU(2|2)×SU(2|2)$\mathit{SU}(2|2)\times \mathit{SU}(2|2)$ symmetry algebra. Also for the open string ending on the Y=0$Y=0$ brane, we reproduce the unique vacuum state from the fermion zero-modes.     

The Harari–Shupe preon model and nonrelativistic quantum phase space

We propose that the whole algebraic structure of the Harari–Shupe rishon model originates via a Dirac-like linearization of quadratic form x²+p²${\mathbf{x}}^2+{\mathbf{p}}^2$, with position and momentum satisfying standard commutation relations. The scheme does not invoke the concept of preons as spin-1/2 subparticles, thus evading the problem of preon confinement, while fully explaining all symmetries emboded in the Harari–Shupe model. Furthermore, the concept of quark colour is naturally linked to the ordering of rishons. Our scheme leads to group U(1)⊗SU(3)$U(1)\otimes \mathit{SU}(3)$ combined with SU(2)$\mathit{SU}(2)$, with two of the SU(2)$\mathit{SU}(2)$ generators not commuting with reflections. An interpretation of intra-generation quark–lepton transformations in terms of genuine rotations and reflections in phase space is proposed.     

Field strength formulation,lattice Bianchi identities and perturbation theory for non-Abelian models

We develop an analytical approach for studying lattice gauge theories within the plaquette representation where the plaquette matrices play the role of the fundamental degrees of freedom. We start from the original Batrouni formulation and show how it can be modified in such a way that each non-Abelian Bianchi identity contains only two connectors instead of four. In addition, we include dynamical fermions in the plaquette formulation. Using this representation we construct the low-temperature perturbative expansion for U(1)$U(1)$ and SU(N)$\mathit{SU}(N)$ models and discuss its uniformity in the volume. The final aim of this study is to give a mathematical background for working with non-Abelian models in the plaquette formulation.     

Two-component gadget for transforming any two nonorthogonal polarization states into one another

We present an algorithm for transforming an arbitrary input polarization state into a nonorthogonal but otherwise arbitrary output polarization state, by using two quarter-wave retarders. Such an array reduces the number of retarders employed in the well-known Simon–Mukunda gadget, which consists of one half-wave and two quarter-wave retarders. The latter was designed to realize arbitrary SU(2)$\mathit{SU}(2)$ transformations on qubits. The gadget presented here accomplishes a related task, allowing to transforming an input qubit into a target qubit, by choosing a particular SU(2)$\mathit{SU}(2)$ transformation that is realizable with two quarter-wave plates.     

Matrix regularization of embedded 4-manifolds

We consider products of two 2-manifolds such as S²×S²$S^2\times S^2$, embedded in Euclidean space and show that the corresponding 4-volume preserving diffeomorphism algebra can be approximated by a tensor product SU(N)⊗SU(N)$\mathit{SU}(N)\otimes \mathit{SU}(N)$ i.e. functions on a manifold are approximated by the Kronecker product of two SU(N)$\mathit{SU}(N)$ matrices.     

Two-dimensional gauge theory and matrix model

We study a matrix model obtained by dimensionally reducing Chern–Simons theory on S³$S^3$. We find that the matrix integration is decomposed into sectors classified by the representation of SU(2)$\mathit{SU}(2)$. We show that the N  -block sectors reproduce SU(N)$\mathit{SU}(N)$ Yang–Mills theory on S²$S^2$ as the matrix size goes to infinity.     

What is the minimal supersymmetric Standard Model from F-theory?

We construct gauge theory of SU(3)×SU(2)×U(1)$\mathit{SU}(3)\times \mathit{SU}(2)\times U(1)$ by spectral cover from F-theory and ask how the Standard Model is extended under minimal assumptions on Higgs sector. For the requirement on different numbers between Higgs pairs and matter generations (respectively one and three) distinguished by R-parity, we choose a universal G  -flux obeying SO(10)$\mathit{SO}(10)$ but slightly breaking _E6$E_6$ unification relation. This condition forces distinction between up and down Higgs fields, suppression of proton decay operators up to dimension five, and existence and dynamics of a singlet related to μ-parameter.     

Towards a Loop Quantum Gravity and Yang–Mills unification

We propose a new method of unifying gravity and the Standard Model by introducing a spin-foam model. We realize a unification between an SU(2)$\mathit{SU}(2)$ Yang–Mills interaction and 3D   general relativity by considering a constrained Spin(4)∼SO(4)$\mathrm{Spin}(4)\sim \mathit{SO}(4)$ Plebanski action. The theory is quantized à la   spin-foam by implementing the analogue of the simplicial constraints for the Spin(4)$\mathrm{Spin}(4)$ symmetry, providing a way to couple Yang–Mills fields to spin-foams. A natural 4D extension of the theory is introduced. We also present a way to recover 2-point correlation functions between the connections as a first way to implement scattering amplitudes between particle states, aiming to connect Loop Quantum Gravity to new physical predictions.     

The QCD spin chain S matrix

Beisert et al. have identified an integrable SU(2,2)$\mathit{SU}(2,2)$ quantum spin chain which gives the one-loop anomalous dimensions of certain operators in large Nc$N_c$ QCD. We derive a set of nonlinear integral equations (NLIEs) for this model, and compute the scattering matrix of the various (in particular, magnon) excitations.     

Symbiotic symmetries of the two-Higgs-doublet model

The new phenomenon of symbiotic symmetries   is described in the context of the Two-Higgs-Doublet Model (THDM). The quartic potential has two or more separate sectors with unequal symmetries, but these unequal symmetries persist even though the different sectors are renormalized by one another. We discuss all such symmetries of the THDM, consistent with the SU(2)×U(1)$\mathit{SU}(2)\times U(1)$ gauge interactions, using the Pauli formalism.     

Geometric measure of pairwise quantum discord for superpositions of multipartite generalized coherent states

We give the explicit expressions of the pairwise quantum correlations present in superpositions of multipartite coherent states. A special attention is devoted to the evaluation of the geometric quantum discord. The dynamics of quantum correlations under a dephasing channel is analyzed. A comparison of geometric measure of quantum discord with that of concurrence shows that quantum discord in multipartite coherent states is more resilient to dissipative environments than is quantum entanglement. To illustrate our results, we consider some special superpositions of Weyl–Heisenberg, SU(2)$\mathit{SU}(2)$ and SU(1,1)$\mathit{SU}(1,1)$ coherent states which interpolate between Werner and Greenberger–Horne–Zeilinger states.     

Type II seesaw mechanism for Higgs doublets and the scale of new physics

We elaborate on an earlier proposal by Ernest Ma of a type II seesaw mechanism for suppressing the vacuum expectation values of some Higgs doublets. We emphasize that, by nesting this form of seesaw mechanism into various other seesaw mechanisms, one may obtain light neutrino masses in such a way that the new-physics scale present in the seesaw mechanism—the masses of scalar gauge-SU(2)$\mathit{SU}(2)$ triplets, scalar SU(2)$\mathit{SU}(2)$ doublets, or right-handed neutrinos—does not need to be higher than a few 10 TeV. We also investigate other usages of the type II seesaw mechanism for Higgs doublets. For instance, the suppression of the vacuum expectation values of Higgs doublets may realize Froggatt–Nielsen suppression factors in some entries of the fermion mass matrices.     

Generalizing minimal supergravity

In Grand Unified Theories (GUTs), the Standard Model (SM) gauge couplings need not be unified at the GUT scale due to the high-dimensional operators. Considering gravity mediated supersymmetry breaking, we study for the first time the generic gauge coupling relations at the GUT scale, and the general gaugino mass relations which are valid from the GUT scale to the electroweak scale at one loop. We define the index k   for these relations, which can be calculated in GUTs and can be determined at the Large Hadron Collider and the future International Linear Collider. Thus, we give a concrete definition of the GUT scale in these theories, and suggest a new way to test general GUTs at future experiments. We also discuss five special scenarios with interesting possibilities. With our generic formulae, we present all the GUT-scale gauge coupling relations and all the gaugino mass relations in the SU(5)$\mathit{SU}(5)$ and SO(10)$\mathit{SO}(10)$ models, and calculate the corresponding indices k. Especially, the index k   is 5/3 in the traditional SU(5)$\mathit{SU}(5)$ and SO(10)$\mathit{SO}(10)$ models that have been studied extensively so far. Furthermore, we discuss the field theory realization of the U(1)$U(1)$ flux effects on the SM gauge kinetic functions in F-theory GUTs, and calculate their indices k as well.     

Multiple layer structure of non-Abelian vortex

Bogomolny–Prasad–Sommerfield (BPS) vortices in U(N)$U(N)$ gauge theories have two layers corresponding to non-Abelian and Abelian fluxes, whose widths depend nontrivially on the ratio of U(1)$U(1)$ and SU(N)$\mathit{SU}(N)$ gauge couplings. We find numerically and analytically that the widths differ significantly from the Compton lengths of lightest massive particles with the appropriate quantum number.     

Supersymmetric quantum mechanics of magnetic monopoles: A case study

We study, in detail, the supersymmetric quantum mechanics of charge-(1,1)$(1,1)$ monopoles in N=2$N=2$ supersymmetric Yang–Mills–Higgs theory with gauge group SU(3)$\mathit{SU}(3)$ spontaneously broken to U(1)×U(1)$U(1)\times U(1)$. We use the moduli space approximation of the quantised dynamics, which can be expressed in two equivalent formalisms: either one describes quantum states by Dirac spinors on the moduli space, in which case the Hamiltonian is the square of the Dirac operator, or one works with anti-holomorphic forms on the moduli space, in which case the Hamiltonian is the Laplacian acting on forms. We review the derivation of both formalisms, explicitly exhibit their equivalence and derive general expressions for the supercharges as differential operators in both formalisms. We propose a general expression for the total angular momentum operator as a differential operator, and check its commutation relations with the supercharges. Using the known metric structure of the moduli space of charge-(1,1)$(1,1)$ monopoles we show that there are no quantum bound states of such monopoles in the moduli space approximation. We exhibit scattering states and compute corresponding differential cross sections.