Large-Nf chiral transition in the Yukawa model

We investigate the finite-temperature behavior of the Yukawa model in which $N_f$ fermions are coupled with a scalar field ϕ in the limit $N_f\to \infty$. Close to the chiral transition the model shows a crossover between mean-field behavior (observed for $N_f=\infty$) and Ising behavior (observed for any finite $N_f$). We show that this crossover is universal and related to that observed in the weakly-coupled ${\varphi }^4$ theory. It corresponds to the renormalization-group flow from the unstable Gaussian fixed point to the stable Ising fixed point. This equivalence allows us to use results obtained in field theory and in medium-range spin models to compute Yukawa correlation functions in the crossover regime.     

Towards an asymptotic-safety scenario for chiral Yukawa systems

We search for asymptotic safety in a Yukawa system with a chiral U(N _L)_L? ??U(1)_R symmetry, serving as a toy model for the standard-model Higgs sector. Using the functional RG as a nonperturbative tool, the leading-order derivative expansion exhibits admissible non-Gaußian fixed points for 1≤N _L≤57 which arise from a conformal threshold behavior induced by self-balanced boson-fermion fluctuations. If present in the full theory, the fixed point would solve the triviality problem. Moreover, as one fixed point has only one relevant direction even with a reduced hierarchy problem, the Higgs mass as well as the top mass are a prediction of the theory in terms of the Higgs vacuum expectation value. In our toy model, the fixed point is destabilized at higher order due to massless Goldstone and fermion fluctuations, which are particular to our model and have no analogue in the standard model.     

Yukawa coupling structure in intersecting D-brane models

The structure of Yukawa coupling matrices is investigated in type IIA T ⁶/(Z₂ x Z₂) orientifold models with intersecting D-branes. Yukawa coupling matrices are difficult to be made realistic in conventional models in which the generation structure emerges by the multiple intersection of D-branes in the factorized T ⁶ = T ² x T ² x T ². We study the new type of flavor structure, where Yukawa couplings are dynamically generated, and show this type of models lead to non-trivial structures of Yukawa coupling matrices, which can be realistic.Received: 8 December 2004, Revised: 22 December 2004, Published online: 9 March 2005     

Solid-state NMR characterization of diastereoisomeric chiral stationary phases and their soluble models

Two diastereoisomeric chiral stationary phases (CSPs), devised for enantioselective HPLC, showing unexplained differences in their chromatographic performances, have been characterized, together with their soluble models, by means of ¹³C-cross polarization/magic angle spinning (CP/MAS), ¹H-MAS and ¹H-free induction decay (FID) analysis. The NMR investigation of the soluble models has not highlighted significant structural/conformational differences between the two diastereoisomers, but has constituted a useful support for the analysis of the more complex NMR data of the CSPs. The organic chiral selectors of the stationary phases show a poor internal mobility and no conformational differences between the two diastereoisomers have been observed. On the contrary, interesting differences between the two CSPs have been found involving the silanols on the silica surface and the dynamics of the linking chains between the organic selectors and the silica surface itself. An explanation of the chromatographic behaviour has been proposed in terms of different proximity of the organic moieties with respect to the inorganic surface in the two CSPs.     

Dynamical symmetry breaking in models with the Yukawa interaction

The models with a massless fermion and a self-interacting massive scalar field with the Yukawa interaction are discussed. The chiral condensate and the fermion mass are calculated analytically through a one-loop approximation in (1 + 1)-dimensions. It is shown that the models have a phase transition as a function of the squared mass of the scalar field.     

Inhomogeneous chiral symmetry breaking phases

We investigate inhomogeneous chiral symmetry breaking phases in the phase diagram of the two-flavor Nambu-Jona-Lasinio model, concentrating on phases with one-dimensional modulations. It is found that the first-order transition line in the phase diagram of homogeneous phases gets completely covered by an inhomogeneous phase which is bordered by second-order transition lines. The inhomogeneous phase turns out to be remarkably stable when vector interactions are included.     

Infra-red stable fixed points of Yukawa couplings in supersymmetric models

We provide the solutions of the fixed point conditions of the Yukawa sector for a large class of N = 1 supersymmetric theories including the minimal and next-to-minimal supersymmetric standard models and their grand unified and other extensions. We also introduce a test which can discriminate between infra-red stable, infra-red unstable and saddle point solutions, and illustrate our methods with the example of the next-to-minimal supersymmetric standard model. We show that in this case, the fixed point prediction of the top quark mass is equivalent to that of the minimal supersymmetric standard model, supporting previous numerical analyses.     

Insights on some chiral smectic phases

Combining layered positional order as smectic order and chirality can generate complex architectures since twist parallel to the layers is not allowed. This paper will review some new experimental results on different phases resulting from the competition between smectic positional order and twist orientational order. It concerns the TGB_A and the NL^*, that is the liquid line phase as well as the SmQ phase. Chiral effects in the isotropic phase will also be discussed.     

Algebraic models of local period maps and Yukawa algebras

We describe some \(L_{\infty }\) model for the local period map of a compact Kähler manifold. Applications include the study of deformations with associated variation of Hodge structure constrained by certain closed strata of the Grassmannian of the de Rham cohomology. As a by-product, we obtain an interpretation in the framework of deformation theory of the Yukawa coupling.     

Instanton-like solutions in chiral models

General two-dimensional Euclidean chiral models of field theory are considered in detail. It is shown that in the case when the field takes its values in an arbitrary Kähler manifold the “duality equations” reduce to the Cauchy- Riemann equations on this manifold. For homogeneous manifolds the solutions of these equations do exist and are given by rational functions.     

Pentaquarks in chiral soliton models

The spectra of pentaquarks, some of them observed recently, are discussed within the topological soliton model and compared with the simplified quark picture. The results obtained within the chiral soliton model depend to some extent on the quantization scheme: rigid rotator, soft rotator, or bound state model. The similarity of the spectra of baryon resonances obtained within the quark model and the chiral soliton model is pointed out, although certain differences take place as well, which require careful interpretation. In particular, considerable variation of the strange antiquark mass in different SU(3) multiplets of pentaquarks is required to fit their spectra obtained from chiral solitons. Certain difference in the masses of “good” and “bad” diquarks is required as well, in qualitative agreement with previously made estimates. The partners of exotic states with different values of spin which belong to higher SU(3) multiplets have energy considerably higher than the states with the lowest spin, and this could be a point where the difference from simple quark models is striking. The antiflavor excitation energies for multibaryons are estimated as well, and the binding energies of gJ-hypernuclei and anticharm (antibeauty) hypernuclei are presented for several baryon numbers. Some deficiencies are pointed out in the arguments in the literature against the validity of the chiral soliton approach and/or the SU(3) quantization models. Based partly on the talks presented at the International Seminar on High Energy Physics Quarks-2004, Pushkinogorie, Russia, May 24–30, 2004; International Workshop on Quantum Field Theory and High Energy Physics QFTHEP-04, Saint-Petersburg, Russia, June 17–23, 2004, and Symposium of London Mathematical Society “Topological Solitons and their Applications,” Durham, UK, August 2–12, 2004. A slightly reduced version of this paper is available as E-print HEP-PH/0507028. The text was submitted by the author in English.     

Molecular structure and chiral liquid crystalline phases

We describe briefly some results obtained on both chiral and achiral compounds exhibiting chiral mesophases. We report the first example of a single component system exhibiting the undulated twist grain boundary C* or UTGB _C* phase. Preliminary results concerning a few achiral compounds composed of banana-shaped molecules exhibiting a mesophase is reported. They have been investigated by polarized light optical microscopy, differential scanning calorimetry and x-ray diffraction studies.     

Large N phases of chiral QCD2

A matrix model is constructed which describes a chiral version of the large NU (N) gauge theory on a two-dimensional sphere of area A. This theory has three separate phases. The large area phase describes the associated chiral string theory. An exact expression for the free energy in the large area phase is used to derive a remarkably simple formula for the number of topologically inequivalent covering maps of a sphere with fixed branch points and degree n.