Spectrum of orientifold QCD in the strong coupling and hopping expansion approximation

We use the strong coupling and hopping parameter expansions to calculate the pion and rho meson masses for lattice Yang–Mills gauge theories with fermions in irreducible two-index representations, namely the adjoint, symmetric and antisymmetric. The results are found to be consistent with orientifold planar equivalence, and leading order 1/Nc$1/N_c$ corrections are calculated in the lattice phase. An estimate of the critical bare mass, for which the pion is massless, is obtained as a function of the bare coupling. A comparison to data from the two-flavour SU(2)$\mathit{SU}(2)$ theory with adjoint fermions gives evidence for a bulk phase transition at βc∼2${\beta }_c\sim 2$, separating a pure lattice phase from a phase smoothly connected to the continuum.     

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.     

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.     

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.     

Confined hidden vector dark matter

We argue that the lightest vector bound states of a confining hidden sector communicating with the Standard Model through the Higgs portal are stable and are viable candidates of dark matter. The model is based on an SU(2)$\mathit{SU}(2)$ gauge group with a scalar field in its fundamental representation and the stability of the lightest vector bound state results from the existence of a custodial symmetry. As the relic density depends essentially on the scale of confinement in the hidden sector, ΛHS${\Lambda }_{\mathrm{HS}}$, agreement with WMAP abundance requires ΛHS${\Lambda }_{\mathrm{HS}}$ in the 20–120 TeV range.     

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.     

Towards the MSSM from F-theory

We study the MSSM in F-theory. Its group is the commutant to a structure group SU(5)×UY₍₁₎$\mathit{SU}(5)\times U{(1)}_Y$ of a gauge bundle in E₈$E_8$. The spectrum contains three generations of quarks and leptons plus vectorlike electroweak and colored Higgses. The minimal MSSM Yukawa couplings with matter parity is obtained at the renormalizable level.     

First-order density matrices in one dimension for independent fermions and impenetrable bosons in harmonic traps

To complement existing knowledge of the density matrix γF(x,y)${\gamma }_{\mathrm{F}}(x,y)$ of independent fermions for N   particles in one dimension under harmonic confinement, the corresponding matrix γIB(x,y)${\gamma }_{\mathrm{IB}}(x,y)$ for impenetrable bosons is given for N=2$N=2$ and 3 (with the N=4$N=4$ form available also). For fermions the momentum density is then obtained and illustrated numerically for N=10$N=10$. The boson momentum density is studied analytically at high momentum p  , the coefficients of the p⁻⁴$p^{\mathrm{-4}}$ and p⁻⁶$p^{\mathrm{-6}}$ terms being tabulated for N=2–5$N=2\text{–}5$ inclusive. Their dependence on powers of N   is exhibited numerically. Finally, the functional relationship between γIB(x,y)${\gamma }_{\mathrm{IB}}(x,y)$ and γF(x,y)${\gamma }_{\mathrm{F}}(x,y)$ is formally set out and illustrated.     

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.     

Mini little Higgs and dark matter

We construct a little Higgs model with the most minimal extension of the standard model gauge group by an extra U(1)$U(1)$ gauge symmetry. For specific charge assignments of scalars, an approximate U(3)$U(3)$ global symmetry appears in the cutoff-squared scalar mass terms generated from gauge bosons at one-loop level. Hence, the Higgs boson, identified as a pseudo-Goldstone boson of the broken global symmetry, has its mass radiatively protected up to scales of 5–10 TeV. In this model, a Z₂$Z_2$ symmetry, ensuring the two U(1)$U(1)$ gauge groups to be identical, also makes the extra massive neutral gauge boson stable and a viable dark matter candidate with a promising prospect of direct detection.     

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.     

Chiral extrapolation and determination of low-energy constants from lattice data

We propose analytic approximations of chiral SU(3)$\mathit{SU}(3)$ amplitudes for the extrapolation of lattice data to the physical meson masses. The method allows the determination of NNLO low-energy constants in a controllable fashion. We test the approach with recent lattice data for the ratio FK/Fπ$F_K/F_{\pi }$ of meson decay constants.     

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.     

Adiabatic sound velocity and compressibility of a trapped d-dimensional ideal anyon gas

The adiabatic sound velocity and compressibility for harmonically trapped ideal anyons in arbitrary dimensions are calculated within Haldane fractional exclusion statistics. The corresponding low-temperature and high-temperature behaviors are studied in detail. To compare with the experimental result of unitary fermions, the sound velocity for anyons in the cigar-shaped trap is derived. The sound velocity for anyons in the disk-shaped trap is also calculated. With the parameter g=0.287$g=0.287$, the sound velocity of cigar-shaped unitary fermions modeled by anyons is in good agreement with the experimental result, while that of disk-shaped unitary fermions is v₀/vF=0.406$v_0/v_F=0.406$ with Fermi velocity vF$v_F$.     

Competing orders in one-dimensional half-integer fermionic cold atoms: A conformal field theory approach

The physical properties of arbitrary half-integer spins F=N−1/2$F=N-1/2$ fermionic cold atoms loaded into a one-dimensional optical lattice are investigated by means of a conformal field theory approach. We show that for attractive interactions two different superfluid phases emerge for F?3/2$F?3/2$: A BCS pairing phase, and a molecular superfluid phase which is formed from bound-states made of 2N   fermions. In the low-energy approach, the competition between these instabilities and charge-density waves is described in terms of ZN${\mathbb{Z}}_N$ parafermionic degrees of freedom. The quantum phase transition for F=3/2,5/2$F=3/2,5/2$ is universal and shown to belong to the Ising and three-state Potts universality classes respectively. In contrast, for F?7/2$F?7/2$, the transition is non-universal. For a filling of one atom per site, a Mott transition occurs and the nature of the possible Mott-insulating phases are determined.