Fixed point resolution in extensions of permutation orbifolds

We determine the simple currents and fixed points of the orbifold theory CFT⊗CFT/Z₂$\mathit{CFT}\otimes \mathit{CFT}/{\mathbb{Z}}_2$, given the simple currents and fixed point of the original CFT  . We see in detail how this works for the SUk₍₂₎$\mathit{SU}{(2)}_k$ WZW model, focusing on the field content (i.e. h  -spectrum of the primary fields) of the theory. We also look at the fixed point resolution of the simple current extended orbifold theory and determine the SJ$S^J$ matrices associated to each simple current for SU₂₍₂₎$\mathit{SU}{(2)}_2$ and for the B_1(n)$B{(n)}_1$ and D_1(n)$D{(n)}_1$ series.     

Generalised leptonic colour

It is conceivable that there is an SU?_(N)$\mathit{SU}{(N)}_{?}$ ‘colour’ gauge group for leptons, analogous to the gauged SUq₍₃₎$\mathit{SU}{(3)}_q$ colour group of the quarks. The standard model emerges as the low energy effective theory when the leptonic colour is spontaneously broken. The simplest such generalised leptonic colour models are constructed. We show that the see-saw mechanism for small neutrino masses, along with the theoretical constraint of electric charge quantisation, suggests that the models with N=3$N=3$, 5, 7 are the theoretically most promising cases. A striking feature of generalised leptonic colour is the physics associated with the extra leptonic degrees of freedom—the liptons. These particles can potentially be discovered at future colliders, such as the LHC, making the idea testable in the near future.     

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 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.     

Self-duality of the compactified Ruijsenaars–Schneider system from quasi-Hamiltonian reduction

The Delzant theorem of symplectic topology is used to derive the completely integrable compactified Ruijsenaars–Schneider _IIIb${\mathrm{III}}_{\mathrm{b}}$ system from a quasi-Hamiltonian reduction of the internally fused double SU(n)×SU(n)$\mathit{SU}(n)\times \mathit{SU}(n)$. In particular, the reduced spectral functions depending respectively on the first and second SU(n)$\mathit{SU}(n)$ factor of the double engender two toric moment maps on the _IIIb${\mathrm{III}}_{\mathrm{b}}$ phase space CP(n−1)$\mathbb{C}P(n-1)$ that play the roles of action-variables and particle-positions. A suitable central extension of the SL(2,Z)$\mathit{SL}(2,\mathbb{Z})$ mapping class group of the torus with one boundary component is shown to act on the quasi-Hamiltonian double by automorphisms and, upon reduction, the standard generator S   of the mapping class group is proved to descend to the Ruijsenaars self-duality symplectomorphism that exchanges the toric moment maps. We give also two new presentations of this duality map: one as the composition of two Delzant symplectomorphisms and the other as the composition of three Dehn twist symplectomorphisms realized by Goldman twist flows. Through the well-known relation between quasi-Hamiltonian manifolds and moduli spaces, our results rigorously establish the validity of the interpretation [going back to Gorsky and Nekrasov] of the _IIIb${\mathrm{III}}_{\mathrm{b}}$ system in terms of flat SU(n)$\mathit{SU}(n)$ connections on the one-holed torus.     

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.     

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.     

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)$\mathit{SU}(3)$.     

Discrete gauge symmetries in discrete MSSM-like orientifolds

Motivated by the necessity of discrete _ZN${\mathbb{Z}}_N$ symmetries in the MSSM to insure baryon stability, we study the origin of discrete gauge symmetries from open string sector U(1)$U(1)$?s in orientifolds based on rational conformal field theory. By means of an explicit construction, we find an integral basis for the couplings of axions and U(1)$U(1)$ factors for all simple current MIPFs and orientifolds of all 168 Gepner models, a total of 32 990 distinct cases. We discuss how the presence of discrete symmetries surviving as a subgroup of broken U(1)$U(1)$?s can be derived using this basis. We apply this procedure to models with MSSM chiral spectrum, concretely to all known U(3)×U(2)×U(1)×U(1)$U(3)\times U(2)\times U(1)\times U(1)$ and U(3)×Sp(2)×U(1)×U(1)$U(3)\times \mathit{Sp}(2)\times U(1)\times U(1)$ configurations with chiral bi-fundamentals, but no chiral tensors, as well as some SU(5)$\mathit{SU}(5)$ GUT models. We find examples of models with _Z2${\mathbb{Z}}_2$ (R-parity) and _Z3${\mathbb{Z}}_3$ symmetries that forbid certain B and/or L violating MSSM couplings. Their presence is however relatively rare, at the level of a few percent of all cases.     

Parity doubling among the baryons

We study the evidence for and possible origins of parity doubling among the baryons. First we explore the experimental evidence, finding a significant signal for parity doubling in the non-strange baryons, but little evidence among strange baryons. Next we discuss potential explanations for this phenomenon. Possibilities include suppression of the violation of the flavor singlet axial symmetry (U(1_)A$U(1{)}_A$) of QCD, which is broken by the triangle anomaly and by quark masses. A conventional Wigner–Weyl realization of the SU(2_)L×SU(2_)R$\mathit{SU}(2{)}_L\times \mathit{SU}(2{)}_R$ chiral symmetry would also result in parity doubling. However this requires the suppression of families of chirally invariant   operators by some other dynamical mechanism. In this scenario the parity doubled states should decouple from pions. We discuss other explanations including connections to chiral invariant short distance physics motivated by large _Nc$N_c$ arguments as suggested by Shifman and others, and intrinsic deformation of relatively rigid highly excited hadrons, leading to parity doubling on the leading Regge trajectory. Finally we review the spectroscopic consequences of chiral symmetry using a formalism introduced by Weinberg, and use it to describe two baryons of opposite parity.     

Inverted neutrino mass hierarchy and new signals of a chromophobic charged Higgs at the Large Hadron Collider

We explore the signals of a charged Higgs arising in a two Higgs doublet model respecting SUL₍₂₎×U(1)×Z₂$\mathit{SU}{(2)}_L\times U(1)\times Z_2$ symmetry with three singlet right-handed neutrinos, NR$N_R$. The charged Higgs in this model has negligible coupling with quarks, and has unsuppressed coupling to leptons and neutrinos. This leads to novel signatures of the charged Higgs at the LHC, especially in the case of an inverted neutrino mass hierarchy, in the form of electrons and muons with missing energy.     

On neutrino masses via CPT violating Higgs interaction in the Standard Model

The Lorentz invariant CPT   violation by using non-local interactions is naturally incorporated in the Higgs coupling to neutrinos in the Standard Model, without spoiling the basic SU_(2)L×U(1)$\mathit{SU}{(2)}_L\times U(1)$ gauge symmetry. The neutrino–antineutrino mass splitting is thus realized by the mechanism which was proposed recently, assuming the neutrino masses to be predominantly Dirac-type in the Standard Model.     

Random ballistic growth and diffusion in symmetric spaces

Sequential ballistic deposition (BD) with next-nearest-neighbor (NNN) interactions in a N  -column box is viewed as a time-ordered product of (N×N)$(N\times N)$-matrices consisting of a single _sl2${\mathit{sl}}_2$-block which has a random position along the diagonal. We relate the uniform BD growth with the diffusion in the symmetric space _HN=SL(N,R)/SO(N)$H_N=\mathit{SL}(N,R)/\mathit{SO}(N)$. In particular, the distribution of the maximal height of a growing heap is connected with the distribution of the maximal distance for the diffusion process in _HN$H_N$. The coordinates of _HN$H_N$ are interpreted as the coordinates of particles of the one-dimensional Toda chain. The group-theoretic structure of the system and links to some random matrix models are also discussed.     

Differential operator realizations of superalgebras and free field representations of corresponding current algebras

Based on the particular orderings introduced for the positive roots of finite-dimensional basic Lie superalgebras, we construct the explicit differential operator representations of the osp(2r|2n)$\mathit{osp}(2r|2n)$ and osp(2r+1|2n)$\mathit{osp}(2r+1|2n)$ superalgebras and the explicit free field realizations of the corresponding current superalgebras ospk_(2r|2n)$\mathit{osp}{(2r|2n)}_k$ and ospk_(2r+1|2n)$\mathit{osp}{(2r+1|2n)}_k$ at an arbitrary level k. The free field representations of the corresponding energy–momentum tensors and screening currents of the first kind are also presented.     

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.