International Journal of Modern Physics A

In this paper, we compute the NSVZ beta functions for $\mathcal{𝒩}=1$ four-dimensional quiver theories arising from D-brane probes on singularities, complete with anomalous dimensions, for a large set of phases in the corresponding duality tree. While these beta functions are zero for D-brane probes, they are nonzero in the presence of fractional branes. As a result there is a nontrivial RG behavior. We apply this running of gauge couplings to some toric singularities such as the cones over Hirzebruch and del Pezzo surfaces. We observe the emergence in string theory, of “Duality Walls,” a finite energy scale at which the number of degrees of freedom becomes infinite and beyond which Seiberg duality does not proceed. We also identify certain quiver symmetries as T-duality-like actions in the dual holographic theory.

In the framework of $f(T,\mathcal{𝒯})$ gravity, where T denotes the torsion scalar and $\mathcal{𝒯}$ signifies the energy–momentum tensor’s trace, our study explores the realm of holographic inflation. We employed a holographic potential, incorporating three widely recognized inflationary potentials in cosmological research. Our main objective was to determine the range of parameters that govern the interaction between geometry and matter, which plays a crucial role in describing inflationary phenomena in the universe. By calculating the slow-roll parameters, we were able to forecast critical cosmological quantities, including the scalar spectral index $n_s$, the tensor-to-scalar ratio r and the tensor spectral index $n_T$, all expressed in terms of the potential’s parameters. When comparing these findings with those derived in teleparallel gravity, which is equivalent to General Relativity (GR), we identified the significant impact of the parameter linking geometry and matter. This influence is thoroughly demonstrated through detailed results in various tables, highlighting its role in $f(T,\mathcal{𝒯})$ gravity. Our outcomes underscore the strength of the interaction between geometry and matter while showing considerable alignment with the PLANCK 2018 and WMAP data, thereby reinforcing the reliability and relevance of our conclusions.

We define the generalized vertex operators expressed by charged fermions and state vectors corresponding to the n-partition. The action of the generalized vertex operators on state vectors and the generalized universal character (UC) plane partitions have been investigated by the fermion calculus techniques. Furthermore, we construct the infinite scalar product and the generating function associated with the generalized UC plane partitions.

The L3 Collaboration reported data on 2-jet and 3-jet Bose–Einstein correlations (BECs) with the results obtained through the $\tau$-model in 2011. In this study, we analyze these correlations using the conventional formula with the Gaussian long-range correlation (${\mathrm{\text{CF}}}_{\mathrm{\text{I}}}\times {\mathrm{\text{LRC}}}_{(\mathrm{\text{Gauss}})}$). The estimated ranges of interactions for 2-jet and 3-jet, $R_{\mathrm{\text{2-jet}}}$ and $R_{\mathrm{\text{3-jet}}}$, are almost the same magnitude as those by $\tau$-model: $R_{\mathrm{\text{2-jet}}}=0.83\pm 0.05$ (stat) fm and $R_{\mathrm{\text{3-jet}}}=1.09\pm 0.04$ (stat) fm. The anticorrelation in BEC (less than 1.0) observed by the L3 Collaboration is related to the partially negative density profile (${\rho }_{\tau ,\mathrm{\text{BE}}}(\xi )$ in $\xi$ space) in the $\tau$-model and the ${\mathrm{\text{LRC}}}_{(\mathrm{\text{Gauss}})}=1/(1+\alpha e^{-\beta Q^2})$ in ${\mathrm{\text{CF}}}_{\mathrm{\text{I}}}\times {\mathrm{\text{LRC}}}_{(\mathrm{\text{Gauss}})}$, respectively. Remarkably, the probability $P_{\tau }(\xi )$ calculated from the Levy canonical form exhibits partially negative behavior.

This study is dedicated to the description of the polarized Bjorken sum rule, based on recently derived formulas within the analytic QCD approach. To accommodate the photoproduction limit and incorporate the Gerasimov–Drell–Hearn and Burkhardt-Cottingham sum rules, we develop a new representation for the twist-2 part of the Bjorken sum rule. The derived results were applied for processing of experimental data. We observed a good agreement between the experimental data and the predictions from analytic QCD. In contrast, there is a significant discrepancy between these data and the fitting curves within the standard perturbative approach.

In this paper, we have investigated bound state solutions for a scalar particle described in the space–time of a chiral cosmic string subjected to rotational effects in a Kaluza–Klein theory. We saw that combinations between the parameters that describe the generalized space–time impose upper and lower limits for the radial coordinate leading to well-established boundary conditions.

In this paper, we study the couplings of the gravity supermultiplet (graviton and gravitino) of minimal $\mathcal{𝒩}=1$ supergravity (SUGRA) following a constructive approach. First, we use the master formula that follows from considering the scaling behavior of the spinor variables under the little group. Second, we derive the four-point couplings using the Britto–Cachazo–Feng–Witten (known as BCFW) recursion relations. Then, we verify these results for the general three-point interactions that can be derived using the Kawai–Lewellen–Tye relations (also known as KLT-type relations), i.e. they can be written as the square of the coupling of the gluons and gluinos. Finally, we consider the graviton–gravitino SUGRA Compton effect. For completeness, we present in the appendix the $\mathcal{𝒩}=1$ SUGRA Lagrangian in the two-component Weyl formalism, including proofs of supersymmetry (SUSY) and gauge invariances.