Generalizations of Maxwell (super)algebras by the expansion method

The Lie algebras expansion method is used to show that the four-dimensional spacetime Maxwell (super)algebras and some of their generalizations can be derived in a simple way as particular expansions of o(3,2)$o(3,2)$ and osp(N|4)$\mathit{osp}(N|4)$.     

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.     

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.     

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.     

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 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.     

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)$\mathit{SU}(3)$.     

Exact classical solutions of nonlinear sigma models on supermanifolds

We study two-dimensional nonlinear sigma models with target spaces being the complex super-Grassmannian manifolds, that is, coset supermanifolds G(m,p|n,q)≅U(m|n)/[U(p|q)⊗U(m−p|n−q)]$G(m,p|n,q)\cong U(m|n)/[U(p|q)\otimes U(m-p|n-q)]$ for 0?p?m$0?p?m$, 0?q?n$0?q?n$ and 1?p+q$1?p+q$. The projective superspace CPm−1|n${\mathbf{CP}}^{m-1|n}$ is a special case of p=1$p=1$, q=0$q=0$. For the two-dimensional Euclidean base space, a wide class of exact classical solutions (or harmonic maps) are constructed explicitly and elementarily in terms of Gramm–Schmidt orthonormalisation procedure starting from holomorphic bosonic and fermionic supervector input functions. The construction is a generalisation of the non-super-case published more than twenty years ago by one of the present authors.     

Mass mixing,the fourth generation,and the kinematic Higgs mechanism

We describe how to construct explicit chiral fermion mass terms using Dirac–Kähler (DK) spinors. Classical massive DK spinors are shown to be equivalent to four generations of Dirac spinors with equal mass coupled to a background U(2,2)$U(2,2)$ gauge field. Quantization breaks U(2,2)$U(2,2)$ to U(2)×U(2)$U(2)\times U(2)$, lifts mass spectrum degeneracy, and generates a non-trivial CKM mixing.     

Renormalization in theories with modified dispersion relations: Weak gravitational fields

We consider a free quantum scalar field satisfying modified dispersion relations in curved spacetimes, within the framework of Einstein–Aether theory. Using a power counting analysis, we study the divergences in the adiabatic expansion of 〈?²〉$〈{?}^2〉$ and 〈T_μν〉$〈T_{\mu \nu }〉$, working in the weak field approximation. We show that for dispersion relations containing up to 2s powers of the spatial momentum, the subtraction necessary to renormalize these two quantities on general backgrounds depends on s   in a qualitatively different way: while 〈?²〉$〈{?}^2〉$ becomes convergent for a sufficiently large value of s  , the number of divergent terms in the adiabatic expansion of 〈T_μν〉$〈T_{\mu \nu }〉$ increases with s. This property was not apparent in previous results for spatially homogeneous backgrounds.     

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.     

Spin chains in magnetic field,non-skew-symmetric classical r-matrices and BCS-type integrable systems

We construct generalized Gaudin systems in an external magnetic field corresponding to arbitrary so(3)$\mathit{so}(3)$-valued non-skew-symmetric r-matrices with spectral parameters and non-homogeneous external magnetic fields. In the case of r  -matrices diagonal in the sl(2)$\mathit{sl}(2)$ basis we calculate the spectrum and the eigen-values of the corresponding generalized Gaudin hamiltonians using the algebraic Bethe ansatz. We explicitly consider several one-parametric families of non-skew-symmetric classical r-matrices and the corresponding generalized Gaudin systems in a magnetic field. We apply these results to fermionic systems and obtain a wide class of new integrable fermionic BCS-type hamiltonians.     

Frame-like action and unfolded formulation for massive higher-spin fields

Unfolded equations of motion for symmetric massive bosonic fields of any spin in Minkowski and (A)dS$(A)\mathit{dS}$ spaces are presented. Manifestly gauge invariant action for a spin s?2$s?2$ massive field in any dimension is constructed in terms of gauge invariant curvatures.     

Geometrical CP violation from non-renormalisable scalar potentials

We consider in detail the non-renormalisable scalar potential of three Higgs doublets transforming as an irreducible triplet of Δ(27)$\mathrm{\Delta }(27)$ or Δ(54)$\mathrm{\Delta }(54)$. We start from a renormalisable potential that spontaneously leads to a vacuum with CP-violating phases independent of arbitrary parameters – geometrical CP violation. Then we analyse to arbitrarily high order non-renormalisable terms that are consistent with the symmetry and we demonstrate that inclusion of non-renormalisable terms in the potential can preserve the geometrical CP-violating vacuum.     

Noncompact sigma-models: Large N expansion and thermodynamic limit

Noncompact SO(1,N)$\mathrm{SO}(1,N)$ sigma-models are studied in terms of their large N   expansion in a lattice formulation in dimensions d?2$d?2$. Explicit results for the spin and current two-point functions as well as for the Binder cumulant are presented to next to leading order on a finite lattice. The dynamically generated gap is negative and serves as a coupling-dependent infrared regulator which vanishes in the limit of infinite lattice size. The cancellation of infrared divergences in invariant correlation functions in this limit is nontrivial and is in d=2$d=2$ demonstrated by explicit computation for the above quantities. For the Binder cumulant the thermodynamic limit is finite and is given by 2/(N+1)$2/(N+1)$ in the order considered. Monte Carlo simulations suggest that the remainder is small or zero. The potential implications for “criticality” and “triviality” of the theories in the SO(1,N)$\mathrm{SO}(1,N)$ invariant sector are discussed.