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)$\mathit{SU}(3)$.     

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.     

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.     

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.     

Hadro-charmonium

We argue that relatively compact charmonium states, J/ψ$J/\psi$, ψ(2S)$\psi (2S)$, χc${\chi }_c$, can very likely be bound inside light hadronic matter, in particular inside higher resonances made from light quarks and/or gluons. The charmonium state in such binding essentially retains its properties, so that the bound system decays into light mesons and the particular charmonium resonance. Thus such bound states of a new type, which we call hadro-charmonium, may explain the properties of some of the recently observed resonant peaks, in particular of Y(4.26)$Y(4.26)$, Y(4.32–4.36)$Y(4.32\text{–}4.36)$, Y(4.66)$Y(4.66)$, and Z(4.43)$Z(4.43)$. We discuss further possible implications of the suggested picture for the observed states and existence of other states of hadro-charmonium and hadro-bottomonium.     

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.     

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.     

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.     

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.     

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.     

The nature of ZZ branes

In minimal non-critical string theory we show that the principal (r,s)$(r,s)$ ZZ brane can be viewed as the basic (1,1)$(1,1)$ ZZ boundary state tensored with the (r,s)$(r,s)$ Cardy boundary state. In this sense there exists only one ZZ boundary state, the basic (1,1)$(1,1)$ boundary state.     

The puzzle of apparent linear lattice artifacts in the 2d non-linear σ-model and Symanzik's solution

Lattice artifacts in the 2d O(n) non-linear σ  -model are expected to be of the form O(a²)$\mathrm{O}(a^2)$, and hence it was (when first observed) disturbing that some quantities in the O(3)$\mathrm{O}(3)$ model with various actions show parametrically stronger cutoff dependence, apparently O(a)$\mathrm{O}(a)$, up to very large correlation lengths. In a previous letter Balog et al. (2009) [1] we described the solution to this puzzle. Based on the conventional framework of Symanzik's effective action, we showed that there are logarithmic corrections to the O(a²)$\mathrm{O}(a^2)$ artifacts which are especially large (ln³a${\ln }^{3}a$) for n=3$n=3$ and that such artifacts are consistent with the data. In this paper we supply the technical details of this computation. Results of Monte Carlo simulations using various lattice actions for O(3)$\mathrm{O}(3)$ and O(4)$\mathrm{O}(4)$ are also presented.     

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.