International Journal of Modern Physics A

I recall my encounter with Ken Wilson's lattice gauge theory and review the present status of the idea of large N reduction.

Some time ago, the Faddeev–Jackiw canonical quantization formalism for constrained systems with Grassmann dynamical variables in the field theory context was reviewed. In the present work, the resulting formalism is applied to a classical nonrelativistic U(1) ×U(1) gauge field model that describes the electromagnetic interaction of composite particles in 2+1 dimensions. The model contains a Chern–Simons U(1) field and the electromagnetic field, and it uses either a composite boson system or a composite fermion one. The obtained results are compared with the ones corresponding to the implementation of the Dirac formalism to this model, concluding that the Faddeev–Jackiw and Dirac methods cannot be considered equivalent. A simplified version of the above model is analyzed in the same way, similar to the one used within the framework of condensed matter. In this case, it is observed that when the results obtained by the Faddeev–Jackiw and Dirac methods coincide, the first method is more economical than the second one. For both models, the composite fermion case is explicitly considered.

In this paper, we study a class of grand-canonical partition functions with a kernel depending on a small parameter ϵ. This class is directly relevant to Nekrasov partition functions of 𝒩 = 2 SUSY gauge theories on the 4d Ω-background, for which ϵ is identified with one of the equivariant deformation parameter. In the Nekrasov–Shatashvili limit ϵ→0, we show that the free energy is given by an on-shell effective action. The equations of motion take the form of a TBA equation. The free energy is identified with the Yang–Yang functional of the corresponding system of Bethe roots. We further study the associated canonical model that takes the form of a generalized matrix model. Confinement of the eigenvalues by the short-range potential is observed. In the limit where this confining potential becomes weak, the collective field theory formulation is recovered. Finally, we discuss the connection with the alternative expression of instanton partition functions as sums over Young tableaux.

The finite-sized effect caused by compactified space–time is scrutinized by means of the linear sigma model with constituent quarks at finite temperature T and chemical potential μ, where the compactified spatial dimension with length L is taken along the Oz direction. We find several finite-size effects associated with compactified length L: (a) There are two types of Casimir energy corresponding to two types of quarks, untwisted and twisted quarks. (b) For untwisted quarks, a first-order phase transition emerges at intermediate values of L when the Casimir effect is not taken into account and is enhanced by Casimir energy at small L. (c) For twisted quarks, the phase transition is cross-over everywhere when μ≤200 MeV. When μ> 200 MeV there occurs a first-order phase transition at large L and becomes cross-over at smaller L.

We construct an action for double field theory using a metric connection that is compatible with both the generalised metric and the O_{D, D} structure. The connection is simultaneously torsionful and flat. Using this connection, one may construct a proper covariant derivative for double field theory. We then write the doubled action in terms of the generalised torsion of this connection. This action then exactly reproduces that required for double field theory and gauged supergravity.

Current experiments do not support, as ATLAS and CMS Collaborations at the Large Hadron Collider reported, that the Higgs-like resonance discovered in July 2012 is a pure CP-odd state. We examine a general hZZ vertex which contains CP-even and CP-odd couplings, by studying the process with l₁, l₂ = e or μ, to explore the CP mixed property of the Higgs-like particle. One momentum asymmetry and two angular asymmetries have been analyzed in order to reveal the difference from different CP-couplings. Our study shows that these asymmetries could be interesting observables in the future precise experiments.

The properties of the D-brane fluctuations are investigated using the two types of deformation of the Dirac structure, based on the B-transformation and the β-transformation, respectively. The former gives the standard gauge theory with two-form field strength. The latter gives a nonstandard gauge theory on the Poisson manifold with bivector field strength and the vector field as a gauge potential, where the gauge symmetry is a diffeomorphism generated by the Hamiltonian vector field. The map between the two gauge theories is also constructed with the help of Moser's Lemma and the Magnus expansion. We also investigate the relation to the gauge theory on the noncommutative D-branes.

There are suggestive experimental indications that the leptons, neutrinos, and quarks might be composite and that their structure is described by the quantum group SLq(2). Since the hypothetical preons must be very heavy relative to the masses of the leptons, neutrinos, and quarks, there must be a very strong binding field to permit these composite particles to form. Unfortunately there are no experiments direct enough to establish the order of magnitude needed to make the SLq(2) Lagrangian dynamics quantitative. It is possible, however, to parametrize the preon masses and interactions that would be necessary to stabilize the three particle composite representing the leptons, neutrinos, and quarks. In this note we examine possible parametrizations of the masses and the interactions of these hypothetical structures. We also note an alternative view of SLq(2) preons.

The LHC energies are those at which the asymptotic regime in hadron–hadron diffractive collisions (pp, πp, ππ) might be switched on. Based on results of the Dakhno–Nikonov eikonal model which is a generalization of the Good–Walker eikonal approach for a continuous set of channels, we present a picture for transformation of the constituent quark mode to the black disk one. In the black disk mode , we have a growth of the logarithm squared type for total and elastic cross-sections, σ_tot ~ ln² s and σ_el ~ ln² s and -scaling for diffractive scattering and diffractive dissociation of hadrons. The diffractive dissociation cross-section grows as σ_D ~ ln s, σ_DD ~ ln s, and their relative contribution tends to zero: σ_D/σ_tot → 0, σ_DD/σ_tot → 0. Asymptotic characteristics of diffractive and total cross-sections are universal, and this results in the asymptotical equality of cross-sections for all types of hadrons (the Gribov universality). The energy scale for switching on the asymptotic mode is estimated for different processes.