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1.
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)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)SU(2) and SU(3)SU(3). As a result, we obtain the general form of the decomposition for SU(N)SU(N) gauge link variables and confirm the previous results obtained for SU(2)SU(2) and SU(3)SU(3).  相似文献   

2.
3.
We present explicit BPS field configurations representing one non-Abelian monopole with one minimal weight 't Hooft operator insertion. We explore the SO(3)SO(3) and SU(2)SU(2) gauge groups. In the case of SU(2)SU(2) gauge group the minimal 't Hooft operator can be completely screened by the monopole. If the gauge group is SO(3)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.  相似文献   

4.
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)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.  相似文献   

5.
We construct a natural model of the supersymmetric SU(6)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)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/MGUTTeV/MGUT 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 day1 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)SU(6) unification.  相似文献   

6.
We consider products of two 2-manifolds such as S2×S2S2×S2, 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)SU(N)SU(N) i.e. functions on a manifold are approximated by the Kronecker product of two SU(N)SU(N) matrices.  相似文献   

7.
8.
It is shown that four-dimensional N=1N=1 supersymmetric QCD with massive flavors in the fundamental representation of the gauge group can be realized in the hidden sector of E8×E8E8×E8 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)Spin(10), but the methods are applicable to Spin(Nc)Spin(Nc), SU(Nc)SU(Nc) and Sp(Nc)Sp(Nc) for a wide range of color index NcNc. Hidden sectors of this type can potentially be used as a mechanism to break supersymmetry within the context of heterotic M-theory.  相似文献   

9.
We study a matrix model obtained by dimensionally reducing Chern–Simons theory on S3S3. We find that the matrix integration is decomposed into sectors classified by the representation of SU(2)SU(2). We show that the N  -block sectors reproduce SU(N)SU(N) Yang–Mills theory on S2S2 as the matrix size goes to infinity.  相似文献   

10.
Motivated by the necessity of discrete ZNZN 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)×U(2)×U(1)×U(1) and U(3)×Sp(2)×U(1)×U(1)U(3)×Sp(2)×U(1)×U(1) configurations with chiral bi-fundamentals, but no chiral tensors, as well as some SU(5)SU(5) GUT models. We find examples of models with Z2Z2 (R-parity) and Z3Z3 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.  相似文献   

11.
We study the MSSM in F-theory. Its group is the commutant to a structure group SU(5)×UY(1)SU(5)×U(1)Y of a gauge bundle in E8E8. 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.  相似文献   

12.
The Delzant theorem of symplectic topology is used to derive the completely integrable compactified Ruijsenaars–Schneider IIIbIIIb system from a quasi-Hamiltonian reduction of the internally fused double SU(n)×SU(n)SU(n)×SU(n). In particular, the reduced spectral functions depending respectively on the first and second SU(n)SU(n) factor of the double engender two toric moment maps on the IIIbIIIb phase space CP(n−1)CP(n1) that play the roles of action-variables and particle-positions. A suitable central extension of the SL(2,Z)SL(2,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 IIIbIIIb system in terms of flat SU(n)SU(n) connections on the one-holed torus.  相似文献   

13.
We determine the simple currents and fixed points of the orbifold theory CFTCFT/Z2CFTCFT/Z2, given the simple currents and fixed point of the original CFT  . We see in detail how this works for the SUk(2)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 SJSJ matrices associated to each simple current for SU2(2)SU(2)2 and for the B1(n)B(n)1 and D1(n)D(n)1 series.  相似文献   

14.
We construct gauge theory of SU(3)×SU(2)×U(1)SU(3)×SU(2)×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)SO(10) but slightly breaking E6E6 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.  相似文献   

15.
We study, in detail, the supersymmetric quantum mechanics of charge-(1,1)(1,1) monopoles in N=2N=2 supersymmetric Yang–Mills–Higgs theory with gauge group SU(3)SU(3) spontaneously broken to U(1)×U(1)U(1)×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.  相似文献   

16.
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)SU(5) and SO(10)SO(10) models, and calculate the corresponding indices k. Especially, the index k   is 5/3 in the traditional SU(5)SU(5) and SO(10)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.  相似文献   

17.
We propose a network model with a fixed number of nodes and links and with a dynamic which favors links between nodes differing in connectivity. We observe a phase transition and parameter regimes with degree distributions following power laws, P(k)∼kP(k)k-γ, with γγ ranging from 0.20.2 to 0.50.5, small-world properties, with a network diameter following D(N)∼logND(N)logN and relative high clustering, following C(N)∼1/NC(N)1/N and C(k)∼kC(k)k-α, with αα close to 3. We compare our results with data from real-world protein interaction networks.  相似文献   

18.
19.
Motivated by experiments in nanoscopic systems, we study a generalized Anderson, which consist of two spin degenerate doublets hybridized to a singlet by the promotion of an electron to two conduction bands, as a function of the energy separation δδ between both doublets. For δ=0δ=0 or very large, the model is equivalent to a one-level SU(NN) Anderson model, with N=4N=4 and 2 respectively. We study the evolution of the spectral density for both doublets (ρ(ω)ρ1σ(ω) and ρ(ω)ρ2σ(ω)) and their width in the Kondo limit as δδ is varied, using the non-crossing approximation (NCA). As δδ increases, the peak at the Fermi energy in the spectral density (Kondo peak) splits and the density of the doublet of higher energy ρ(ω)ρ2σ(ω) shifts above the Ferrmi energy. The Kondo temperature TK (determined by the half-width at half maximum of the Kondo peak in density of the doublet of lower energy ρ(ω)ρ1σ(ω)) decreases dramatically. The variation of TK with δδ is reproduced by a simple variational calculation.  相似文献   

20.
We propose a non-supersymmetric SU(5)SU(5) model in which only the third family of fermions are unified. The model remedies the non-unification of the three Standard Model couplings in non-supersymmetric SU(5)SU(5). It also provides a mechanism for baryon number violation which is needed for the baryon asymmetry of the Universe and is not present in the Standard Model. Current experimental constraints on the leptoquark gauge bosons, mediating such baryon and lepton violating interactions in our model, allow their masses to be at the TeV scale. These can be searched for as a () or (tt) resonance at the Large Hadron Collider as predicted in our model.  相似文献   

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