International Journal of Modern Physics A

The two-dimensional minimal supersymmetric sigma models with homogeneous target spaces $G/H$ and chiral fermions of the same chirality are revisited. In particular, we look into the isometry anomalies in $\mathrm{\text{O}}(N)$ and $\mathrm{\text{CP}}(N-1)$ models. These anomalies are generated by fermion loop diagrams which we explicitly calculate. In the case of $\mathrm{\text{O}}(N)$ sigma models the first Pontryagin class vanishes, so there is no global obstruction for the minimal ${𝒩}=(0,1)$ supersymmetrization of these models. We show that at the local level isometries in these models can be made anomaly free by specifying the counterterms explicitly. Thus, there are no obstructions to quantizing the minimal ${𝒩}=(0,1)$ models with the $S^{N-1}=\mathrm{\text{SO}}(N)/\mathrm{\text{SO}}(N-1)$ target space while preserving the isometries. This also includes $\mathrm{\text{CP}}(1)$ (equivalent to $S^2$) which is an exceptional case from the $\mathrm{\text{CP}}(N-1)$ series. For other $\mathrm{\text{CP}}(N-1)$ models, the isometry anomalies cannot be rescued even locally, this leads us to a discussion on the relation between the geometric and gauged formulations of the $\mathrm{\text{CP}}(N-1)$ models to compare the original of different anomalies. A dual formalism of $\mathrm{\text{O}}(N)$ model is also given, in order to show the consistency of our isometry anomaly analysis in different formalisms. The concrete counterterms to be added, however, will be formalism dependent.

The action for a massless particle in 4D Minkowski space–time has a worldline-time reversing symmetry corresponding to CPT invariance of the quantum theory. The analogous symmetry of the ${𝒩}$-extended superparticle is shown to be anomalous when ${𝒩}$ is odd; in the supertwistor formalism this is because a CPT-violating worldline-Chern–Simons term is needed to preserve the chiral $U(1)$ gauge invariance. This accords with the fact that no massless ${𝒩}=1$ super-Poincaré irrep is CPT-self-conjugate. There is a CPT self-conjugate supermultiplet when ${𝒩}$ is even, but it has $2^{{𝒩}+1}$ states when $\frac{1}{2}{𝒩}$ is odd (e.g. the ${𝒩}=2$ hypermultiplet) in contrast to just $2^{{𝒩}}$ when $\frac{1}{2}{𝒩}$ is even (e.g. the ${𝒩}=4$ Maxwell supermultiplet). This is shown to follow from a Kramers degeneracy of the superparticle state space when $\frac{1}{2}{𝒩}$ is odd.

We study the dissipative Hofstadter model on a triangular lattice, making use of the $O(2,2;R)$ T-dual transformation of string theory. The $O(2,2;R)$ dual transformation transcribes the model in a commutative basis into the model in a noncommutative basis. In the zero-temperature limit, the model exhibits an exact duality, which identifies equivalent points on the two-dimensional parameter space of the model. The exact duality also defines magic circles on the parameter space, where the model can be mapped onto the boundary sine-Gordon on a triangular lattice. The model describes the junction of three quantum wires in a uniform magnetic field background. An explicit expression of the equivalence relation, which identifies the points on the two-dimensional parameter space of the model by the exact duality, is obtained. It may help us to understand the structure of the phase diagram of the model.

The processes $e^{+}{e}^{-}\to K^{\pm }{K}^{\ast \mp }(892)$ and $e^{+}{e}^{-}\to \eta \varphi (1020)$ are calculated in the framework of the extended Nambu–Jona-Lasinio model. The intermediate vector mesons $\rho (770)$, $\omega (782)$, $\varphi (1020)$ and their first radially excited states are taken into account. The obtained results are in satisfactory agreement with the experimental data. The predictions for the cross-sections of the reactions $e^{+}{e}^{-}\to K^{\pm }{K}^{\ast \mp }(1410)$, $e^{+}{e}^{-}\to {\eta }^{\prime }(958)\varphi (1020)$ and $e^{+}{e}^{-}\to \eta \varphi (1680)$ were made.

We compute Vassiliev invariants up to order six for arbitrary pretzel knots, which depend on $g+1$ parameters $n_1,\dots ,n_{g+1}$. These invariants are symmetric polynomials in $n_1,\dots ,n_{g+1}$ whose degree coincide with their order. We also discuss their topological and integer-valued properties.

Recently there has been a huge interest in the diphoton excess around 750 GeV reported by both ATLAS and CMS collaborations, although the newest analysis with more statistics does not seem to support the excess. Nevertheless, the diphoton channel at the LHC experiments are a powerful tool to probe a new physics. One of the most natural explanations of a diphoton excess, if it occurs, could be a new scalar boson with exotic colored particles. In this setup, it would be legitimate to ask what is the role of this new scalar in nature. A heavy neutral gauge boson $(Z^{\prime })$ is one of the traditional targets of the discovery at the collider experiments with numerous motivations. While the Landau–Yang theorem dictates the diphoton excess cannot be this spin-1 gauge boson, there is a strong correlation of a new heavy gauge boson and a new scalar boson which provides a mass to the gauge boson being at the same mass scale. In this paper, we point out a simple fact that a new scalar with a property similar to the recently highlighted 750 GeV would suggest an existence of a TeV scale $Z^{\prime }$ gauge boson that might be within the reach of the LHC Run 2 experiments. We take a scenario of the well-motivated and popular gauged $B-L$ symmetry and require the gauge coupling unification to predict the mass and other properties of the $Z^{\prime }$ and illustrate the discovery of the $Z^{\prime }$ would occur during the LHC experiments.