International Journal of Modern Physics A

An overview is presented on the current status of main mathematical computation methods for the multiloop corrections to single-scale observables in quantum field theory and the associated mathematical number and function spaces and algebras. At present, massless single-scale quantities can be calculated analytically in QCD to 4-loop order and single mass and double mass quantities to 3-loop order, while zero-scale quantities have been calculated to 5-loop order. The precision requirements of the planned measurements, particularly at the FCC-ee, form important challenges to theory, and will need important extensions of the presently known methods.

In order to analyze the fidelity susceptibility of nonrelativistic field theories, which are important in condensed matter systems, we generalize the proposal to obtain the fidelity susceptibility holographically to Lifshitz geometries. It will be argued that this proposal can be used to study the fidelity susceptibility for various condensed matter systems. To demonstrate this, we will explicitly use this proposal to analyze the fidelity susceptibility for a nonrelativistic many-body system and argue that the fidelity susceptibility of this theory can be holographically obtained from a bulk Lifshitz geometry. In fact, using an Einstein-Dilaton–Maxwell–AdS–Lifshitz theory, we explicitly demonstrated that the fidelity susceptibility obtained from this bulk geometry is equal to the fidelity susceptibility of a bosonic many-body system.

In this paper, we will compute the holographic complexity (dual to a volume in AdS), holographic fidelity susceptibility and the holographic entanglement entropy (dual to an area in AdS) in a two-dimensional version of AdS which is dual to open strings. We will explicitly demonstrate that these quantities are well defined, and then argue that a relation for fidelity susceptibility and time should hold in general due to the AdS₂ version of the classical Kepler’s principle. We will demonstrate that it holds for AdS₂ solution as well as conformal copies metrics in bulk theory of a prescribed dual conformal invariant quantum mechanics which have been obtained in open string theory. We will also show that hierarchical UV/IR mixing exists in boundary string theory through the holographic bulk picture.

The entropic force experienced by a moving quarkonia in a plasma is computed in a hyperscaling violation background by holography approach. In that case, the axis of the moving quarkonia has an arbitrary angle with wind. We use the results for HSV parameters, which are obtained in our paper, as appropriate values satisfying condition $\mathrm{\text{Im}}{V}_{Q\bar{Q}}<0$. We will show that, in this background, the entropic force of the meson shows a decreasing behavior corresponding to increasing dissociation length. Results of this paper are in agreement with our mentioned work. In addition, we will find diffusion constant in an exact case and by an exact approach which satisfies the mentioned condition in there.

In this paper, we consider the gravitational collapse of generalized Vaidya space–time when the matter satisfies the equation of the state either $P=0$ or $P=-\alpha \rho$, where $0<\alpha <1$. We show that in the case when type I of matter field is dust, then the apparent horizon will never appear but there is no a family of null radial future-directed geodesics which terminate at the central singularity in the past. Also, we show that in the case of negative pressure, the result of the gravitational collapse might be the naked singularity and the apparent horizon appears and in very short time disappears again. In the case of the negative pressure, we show that the result of the gravitational collapse might be the eternal naked singularity.

Within the left–right symmetric model (LRM), the decays

I develop the idea that our world is a brane-like object embedded in Euclidean bulk. In its ground state, the brane constituent matter is assumed to be homogeneous and isotropic, and of negligible influence on the bulk geometry. The analysis of this paper is model independent, in the sense that action functional of bulk fields is not specified. Instead, the behavior of the brane is derived from the universally valid conservation equation of the bulk stress tensor. The present work studies the behavior of a 3-sphere in the five-dimensional Euclidean bulk. The sphere is made of bulk matter characterized by the equation of state $p=\alpha \rho$. It is shown that stability of brane vibrations requires $\alpha <0$. Then, the stable brane perturbations obey Klein–Gordon-like equation with an effective metric of Minkowski signature. The argument is given that it is this effective metric that is detected in physical measurements. The corresponding effective Universe is analyzed for all the values of $\alpha <0$. In particular, the effective metric is shown to be a solution of Einstein’s equations coupled to an effective perfect fluid. As an illustration, one simple choice of the brane constituent matter is studied in detail.

Quantum ${ℛ}$-matrices are the building blocks for the colored HOMFLY polynomials. In the case of three-strand braids with an identical finite-dimensional irreducible representation $T$ of $S{U}_q(N)$ associated with each strand, one needs two matrices: ${{ℛ}}_1$ and ${{ℛ}}_2$. They are related by the Racah matrices ${{ℛ}}_2={𝒰}{{ℛ}}_1{{𝒰}}^{†}$. Since we can always choose the basis so that ${{ℛ}}_1$ is diagonal, the problem is reduced to evaluation of ${{ℛ}}_2$-matrices. This paper is one more step on the road to simplification of such calculations. We found out and proved for some cases that ${{ℛ}}_2$-matrices could be transformed into a block-diagonal ones by the rotation in the sectors of coinciding eigenvalues. The essential condition is that there is a pair of accidentally coinciding eigenvalues among eigenvalues of ${{ℛ}}_1$ matrix. In this case in order to get a block-diagonal matrix, one should rotate the ${{ℛ}}_2$ defined by the Racah matrix in the accidental sector by the angle exactly $\pm \frac{\pi }{4}$.

Recently, it has been suggested that the elements of the S-matrix on the worldvolume of an Abelian D-brane might be in accordance with the Ward identity associated with the T-duality. This shows that by applying linear T-duality, a group of S-matrix elements could be found invariant under such transformations. In this work, we apply the T-duality transformations on the S-matrix elements of one B-field and three NS Abelian gauge fields and find some other Abelian S-matrix elements of one closed and three open string states. Also, we will show that the predicted S-matrix elements are reproduced exactly by explicit calculations.

Projects proposed for the long baseline neutrino and cosmic rays’ experiments require high precision hadron production measurements, using proton beam on different targets, to achieve their physics goals. The predictions of neutrino beam depend on the modeling of protons interacting within the targets. Thus, different hadronic models are being used for this purpose with different precisions, which depend on the projectile protons energy and material of the target used. The comparison of different hadron production models predictions, in proton–carbon interactions at 31 GeV/c, is reported in this paper. Double differential yield of ${\pi }^{\pm }$, $K^{\pm }$ mesons, protons and antiprotons in several polar angle ranges is presented as a function of laboratory momentum. EPOS1.99, EPOS-LHC and QGSJETII-04 models are used to perform simulations. The results of the simulated data are compared with hadron production measurements in proton–carbon interactions at 31 GeV/c performed by the NA61/SHINE experiment at the SPS CERN [Eur. Phys. J. C 76, 84 (2016)]. None of the models completely describes all the distributions. In most of the cases, EPOS1.99 describes the experimental data very well. EPOS-LHC results are also similar in some cases, but QGSJETII-04 predictions failed to reproduce the experimental data.