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)$\mathit{SU}(3)$.     

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.     

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.     

Supersymmetric grand unification with light color-triplet

We construct a natural model of the supersymmetric SU(6)$\mathit{SU}(6)$ unification, in which the symmetry breaking, down to the standard model gauge group, results in the number of pseudo-Nambu–Goldstone superfields with interesting properties. Namely, besides the Higgs doublet–antidoublet pair which is responsible for the electroweak phase transition, the Nambu–Goldstone sector consists of multiplets in the anti- and fundamental representations of SU(5)$\mathit{SU}(5)$. While being strictly massless in the supersymmetric limit, they acquire the weak scale masses as a result of its breaking. The color-triplet components of this light sector could, in principle, mediate an unacceptably fast proton decay; however, because of the natural TeV/_MGUT$\text{TeV}/M_{\mathrm{GUT}}$ suppression of the Yukawa couplings to the light quarks and leptons, their existence is compatible with the experimental bound on proton lifetime. This suppression is made further interesting, since it results in the lifetime, of the lightest of the above-mentioned colored particles from 1 s to 1 day$1\text{day}$, long enough for it to appear stable in the detector. Furthermore, we argue that the accommodation of the color-triplet pseudo-Nambu–Goldstones, without fine-tuning or contradicting observations, implies SU(6)$\mathit{SU}(6)$ unification.     

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.     

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.     

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.     

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.     

Dynamical SUSY breaking in heterotic M-theory

It is shown that four-dimensional N=1$N=1$ supersymmetric QCD with massive flavors in the fundamental representation of the gauge group can be realized in the hidden sector of E₈×E₈$E_8\times E_8$ heterotic string vacua. The number of flavors can be chosen to lie in the range of validity of the free-magnetic dual, using which one can demonstrate the existence of long-lived meta-stable non-supersymmetric vacua. This is shown explicitly for the gauge group Spin(10)$\mathit{Spin}(10)$, but the methods are applicable to Spin(Nc)$\mathit{Spin}(N_c)$, SU(Nc)$\mathit{SU}(N_c)$ and Sp(Nc)$\mathit{Sp}(N_c)$ for a wide range of color index Nc$N_c$. Hidden sectors of this type can potentially be used as a mechanism to break supersymmetry within the context of heterotic M-theory.     

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.     

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.     

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.     

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.     

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.     

Rational r-matrices,higher rank Lie algebras and integrable proton–neutron BCS models

We study integrable cases of pairing BCS hamiltonians containing several types of fermions. We prove that there exist three classes of such integrable models associated with classical rational r  -matrices and Lie algebras gl(2m)$\mathit{gl}(2m)$, sp(2m)$\mathit{sp}(2m)$ and so(2m)$\mathit{so}(2m)$ correspondingly. We diagonalize the constructed hamiltonians by means of the algebraic Bethe ansatz. In the partial case of two types of fermions (m=2$m=2$) the obtained models may be interpreted as N=Z$N=Z$ proton–neutron integrable models. In particular, in the case of sp(4)$\mathit{sp}(4)$ we recover the famous integrable proton–neutron model of Richardson.     

Mean-field gauge interactions in five dimensions II. The orbifold

We study Gauge–Higgs Unification in five dimensions on the lattice by means of the mean-field expansion. We formulate it for the case of an SU(2)$\mathit{SU}(2)$ pure gauge theory and orbifold boundary conditions along the extra dimension, which explicitly break the gauge symmetry to U(1)$U(1)$ on the boundaries. Our main result is that the gauge boson mass computed from the static potential along four-dimensional hyperplanes is non-zero implying spontaneous symmetry breaking. This observation supports earlier data from Monte Carlo simulations in Irges and Knechtli (2007) [12].     

Very special relativity in curved space–times

The generalization of Cohen and Glashow's very special relativity to curved space–times is considered. Gauging the SIM(2)$\mathit{SIM}(2)$ symmetry does not, in general, provide the coupling to the gravitational background. However, locally SIM(2)$\mathit{SIM}(2)$ invariant Lagrangians can always be constructed. For space–times with SIM(2)$\mathit{SIM}(2)$ holonomy, they describe chiral fermions propagating freely as massive particles.