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)$\mathit{SU}(3)$.     

Semiempirical fine-tuning for Hartree–Fock ionization potentials of atomic ions with non-integral atomic number

Amovilli and March (2006) [8] used diffusion quantum Monte Carlo techniques to calculate the non-relativistic ionization potential I(Z)$I(Z)$ in He-like atomic ions for the range of (fractional) nuclear charges Z   lying between the known critical value _Zc=0.911$Z_{\mathrm{c}}=0.911$ at which I(Z)$I(Z)$ tends to zero and Z=2$Z=2$. They showed that it is possible to fit I(Z)$I(Z)$ to a simple quadratic expression. Following that idea, we present here a semiempirical fine-tuning of Hartree–Fock ionization potentials for the isoelectronic series of He, Be, Ne, Mg and Ar-like atomic ions that leads to excellent estimations of _Zc$Z_{\mathrm{c}}$ for these series. The empirical information involved is experimental ionization and electron affinity data. It is clearly demonstrated that Hartree–Fock theory provides an excellent starting point for determining I(Z)$I(Z)$ for these series.     

Atomic parity violation in the economical 3–3–1 model

The deviation δQW$\delta Q_{\mathrm{W}}$ of the weak charge from its standard model prediction due to the mixing of the W boson with the charged bilepton Y as well as of the Z   boson with the neutral Z^′$Z^{\prime }$ and the real part of the non-Hermitian neutral bilepton X   in the economical 3–3–1 model is established. Additional contributions to the usual δQW$\delta Q_{\mathrm{W}}$ expression in the extra U(1)$\mathrm{U}(1)$ models and the left–right models are obtained. Our calculations are quite different from previous analyzes in this kind of the 3–3–1 models and give the limit on mass of the Z^′$Z^{\prime }$ boson, the Z–Z^′$Z\text{–}{Z}^{\prime }$ and W–Y$W\text{–}Y$ mixing angles with the more appropriate values: MZ^′>564 GeV$M_{Z^{\prime }}>564\text{GeV}$, −0.018<sinφ<0$-0.018<\sin \phi <0$ and |sinθ|<0.043$|\sin \theta |<0.043$.     

Is the fragmentation of charm quarks into D mesons described by heavy quark effective theory?

Heavy quark effective theory predicts that produced charm quarks have the same probability to fragment into any of the four D mesons with orbital angular momentum L=0$L=0$: the singlet D state and the triplet D^∗${\mathrm{D}}^{\ast }$ states. This would imply PV(D^∗,D)=3/4${\mathrm{P}}_{\mathrm{V}}({\mathrm{D}}^{\ast },\mathrm{D})=3/4$, where PV${\mathrm{P}}_{\mathrm{V}}$ is the ratio between directly produced L=0$L=0$ vector states (D^∗${\mathrm{D}}^{\ast }$) and all L=0$L=0$ (D and D^∗${\mathrm{D}}^{\ast }$) states. Experimental data collected in several different collision systems (e⁺e⁻${\mathrm{e}}^{+}{\mathrm{e}}^{-}$, hadro-production, photo-production, etc.) and over a broad range of collision energies, show that PV(D^∗,D)=0.594±0.010${\mathrm{P}}_{\mathrm{V}}({\mathrm{D}}^{\ast },\mathrm{D})=0.594\pm 0.010$. From this observation, it follows that “naive spin counting” does not apply to charm production, implying a revision of charm production calculations where this assumption is made.     

What if supersymmetry breaking appears below the GUT scale?

We consider the possibility that the soft supersymmetry-breaking parameters m_1/2$m_{1/2}$ and m₀$m_0$ of the MSSM are universal at some scale Min$M_{\mathrm{in}}$ below the supersymmetric grand unification scale MGUT$M_{\mathrm{GUT}}$, as might occur in scenarios where either the primordial supersymmetry-breaking mechanism or its communication to the observable sector involve a dynamical scale below MGUT$M_{\mathrm{GUT}}$. We analyze the (m_1/2,m₀)$(m_{1/2},m_0)$ planes of such sub-GUT CMSSM models, noting the dependences of phenomenological, experimental and cosmological constraints on Min$M_{\mathrm{in}}$. In particular, we find that the coannihilation, focus-point and rapid-annihilation funnel regions of the GUT-scale CMSSM approach and merge when Min∼¹⁰¹² GeV$M_{\mathrm{in}}\sim {10}^{12}\text{GeV}$. We discuss sparticle spectra and the possible sensitivity of LHC measurements to the value of Min$M_{\mathrm{in}}$.     

Non-Abelian fusion rules from an Abelian system

We demonstrate the emergence of non-Abelian fusion rules for excitations of a two dimensional lattice model built out of Abelian degrees of freedom. It can be considered as an extension of the usual toric code model on a two dimensional lattice augmented with matter fields. It consists of the usual C(Z_p)$\mathbb{C}\left({\mathbb{Z}}_p\right)$ gauge degrees of freedom living on the links together with matter degrees of freedom living on the vertices. The matter part is described by a n$n$ dimensional vector space which we call H_n$H_n$. The Z_p${\mathbb{Z}}_p$ gauge particles act on the vertex particles and thus H_n$H_n$ can be thought of as a C(Z_p)$\mathbb{C}\left({\mathbb{Z}}_p\right)$ module. An exactly solvable model is built with operators acting in this Hilbert space. The vertex excitations for this model are studied and shown to obey non-Abelian fusion rules. We will show this for specific values of n$n$ and p$p$, though we believe this feature holds for all n>p$n>p$. We will see that non-Abelian anyons of the quantum double of C(S₃)$\mathbb{C}\left(S_3\right)$ are obtained as part of the vertex excitations of the model with n=6$n=6$ and p=3$p=3$. Ising anyons are obtained in the model with n=4$n=4$ and p=2$p=2$. The n=3$n=3$ and p=2$p=2$ case is also worked out as this is the simplest model exhibiting non-Abelian fusion rules. Another common feature shared by these models is that the ground states have a higher symmetry than Z_p${\mathbb{Z}}_p$. This makes them possible candidates for realizing quantum computation.     

Fluxmetric and magnetometric demagnetizing factors for cylinders

Fluxmetric and magnetometric demagnetizing factors, _Nf$N_{\mathrm{f}}$ and _Nm$N_{\mathrm{m}}$, for cylinders along the axial direction are numerically calculated as functions of material susceptibility χ$\chi$ and the ratio γ$\gamma$ of length to diameter. The results have an accuracy better than 0.1% with respect to min(_Nf,m,1-_Nf,m)$\min (N_{\mathrm{f},\mathrm{m}},1-N_{\mathrm{f},\mathrm{m}})$ and are tabulated in the range of 0.01?γ?500$0.01?\gamma ?500$ and -1?χ<∞$-1?\chi <\infty$. _Nm$N_{\mathrm{m}}$ along the radial direction is evaluated with a lower accuracy from _Nm$N_{\mathrm{m}}$ along the axis and tabulated in the range of 0.01?γ?1$0.01?\gamma ?1$ and -1?χ<∞$-1?\chi <\infty$. Some previous results are discussed and several applications are explained based on the new results.     

Warped string compactification via singular Calabi–Yau conformal field theory

We construct spacetime supersymmetric, modular invariant partition functions of strings on the conifold-type singularities which include contributions from the discrete-series representations of SL(2,R)$\mathit{SL}(2,\mathbf{R})$. The discrete spectrum is automatically consistent with the GSO projection in the continuous sector, and contains massless matter fields localized on a four-dimensional submanifold at the tip of a cigar. In particular, they are in the 27⊕1$27\oplus 1$ of E₆$E_6$ for the E₈×E₈$E_8\times E_8$ heterotic string. We speculate about a possible realization of local E₆$E_6$ GUT by using this framework.     

Weak mirror symmetry of complex symplectic Lie algebras

A complex symplectic structure on a Lie algebra h$\mathfrak{h}$ is an integrable complex structure J$J$ with a closed non-degenerate (2,0)$(2,0)$-form. It is determined by J$J$ and the real part Ω$\Omega$ of the (2,0)$(2,0)$-form. Suppose that h$\mathfrak{h}$ is a semi-direct product g?V$\mathfrak{g}?V$, and both g$\mathfrak{g}$ and V$V$ are Lagrangian with respect to Ω$\Omega$ and totally real with respect to J$J$. This note shows that g?V$\mathfrak{g}?V$ is its own weak mirror image in the sense that the associated differential Gerstenhaber algebras controlling the extended deformations of Ω$\Omega$ and J$J$ are isomorphic.     

Commuting conformal and dual conformal symmetries in the Regge limit

In this paper we continue our study of the dual SL(2,C)$\mathit{SL}(2,C)$ symmetry of the BFKL equation, analogous to the dual conformal symmetry of N=4$N=4$ super-Yang–Mills. We find that the ordinary and dual SL(2,C)$\mathit{SL}(2,C)$ symmetries do not generate a Yangian, in contrast to the ordinary and dual conformal symmetries in the four-dimensional gauge theory. The algebraic structure is still reminiscent of that of N=4$N=4$ SYM, however, and one can extract a generator from the dual SL(2,C)$\mathit{SL}(2,C)$ close to the bi-local form associated with Yangian algebras. We also discuss the issue of whether the dual SL(2,C)$\mathit{SL}(2,C)$ symmetry, which in its original form is broken by IR effects, is broken in a controlled way, similar to the way the dual conformal symmetry of N=4$N=4$ satisfies an anomalous Ward identity. At least for the lowest orders it seems possible to recover the dual SL(2,C)$\mathit{SL}(2,C)$ by deforming its representation, keeping open the possibility that it is an exact symmetry of BFKL. Independently of a possible relation to N=4$N=4$ scattering amplitudes, this opens an avenue for explaining the integrability of BFKL in terms of two finite-dimensional subalgebras.     

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.     

Standard Model Higgs boson mass from inflation

We analyse one-loop radiative corrections to the inflationary potential in the theory, where inflation is driven by the Standard Model Higgs field. We show that inflation is possible provided the Higgs mass mH$m_H$ lies in the interval mmin<mH<mmax$m_{\min }<m_H<m_{\max }$, where mmin=[136.7+(mt−171.2)×1.95] GeV$m_{\min }=[136.7+(m_t-171.2)\times 1.95]\text{GeV}$, mmax=[184.5+(mt−171.2)×0.5] GeV$m_{\max }=[184.5+(m_t-171.2)\times 0.5]\text{GeV}$ and mt$m_t$ is the mass of the top quark. In the renormalization scheme associated with the Einstein frame the predictions of the spectral index of scalar fluctuations and of the tensor-to-scalar ratio practically do not depend on the Higgs mass within the admitted region and are equal to ns=0.97$n_s=0.97$ and r=0.0034$r=0.0034$ correspondingly.     

A quenched study of the Schrödinger functional with chirally rotated boundary conditions: Non-perturbative tuning

The use of chirally rotated boundary conditions provides a formulation of the Schrödinger functional that is compatible with automatic O(a)$\mathrm{O}(a)$ improvement of Wilson fermions up to O(a)$\mathrm{O}(a)$ boundary contributions. The elimination of bulk O(a)$\mathrm{O}(a)$ effects requires the non-perturbative tuning of the critical mass and one additional boundary counterterm. We present the results of such a tuning in a quenched setup for several values of the renormalized gauge coupling, from perturbative to non-perturbative regimes, and for a range of lattice spacings. We also check that the correct boundary conditions and symmetries are restored in the continuum limit.