International Journal of Modern Physics A

In this paper we exploit Ruelle-type spectral functions and analyze the Verma module over Virasoro algebra, boson–fermion correspondence, the analytic torsion, the Chern–Simons and $\eta$ invariants, as well as the generating function associated to dimensions of the Hochschild homology of the crossed product $ℂ[S_n]⋉{{𝒜}}^{\otimes n}$ (${𝒜}$ is the $q$-Weyl algebra). After analyzing the Chern–Simons and $\eta$ invariants of Dirac operators by using irreducible $SU(n)$-flat connections on locally symmetric manifolds of nonpositive section curvature, we describe the exponential action for the Chern–Simons theory.

We study the texture zeros of $4\times 4$ neutrino mass matrices $M_{\nu }$ in the minimal extended type-I seesaw (MES) mechanism, incorporating one extra gauge singlet field “$S$”. The $4\times 4$  MES model deals with $3\times 3$  $(M_D)$, $3\times 3$  $(M_R)$ and $1\times 3$ mass matrix $(M_S)$ which couples the right-handed neutrinos and the singlet field “$S$”. We carry out the mapping of all possible zero textures of $M_D$, $M_R$ and $M_S$ with the restriction to phenomenologically predictive cases having total eight zeros of $M_D$ and $M_R$ studied in the literature. If $m_s$, the sterile neutrino mass, is subject to any limit, further block diagonalization of $M_{\nu }$ shall not be allowed to reduce it to a $3\times 3$ matrix. In $4\times 4$  $M_{\nu }$ scenario, the study of texture zero is totally different and interesting. With this motivation, we consider the $(4+4)$ scheme where the digits of the pair represent the number of zeros of $M_D$ and $M_R$, respectively, along with the one/two-zero textures of $M_S$. There are a large number of possibilities of zeros of fermion mass matrices, but the implementation of $S_3$ transformations reduces it to a very minimum number of basic structures. As the $4\times 4$ MES matrix is a matrix of rank 3, so we consider only those textures with two zeros which are of rank 3 whereby the number of feasible zero textures reduces to 12, out of 15. On realizing these 12 textures under MES mechanism with $(4+4)$ picture, we arrive at certain correlations for each texture. We examine the viability of each texture by scanning their respective correlations under recent neutrino oscillation data. Also, we discuss the interplay of Dirac and Majorana CP phases in determining the viability of a texture. The allowed two-zero textures are finally realized using a discrete Abelian flavor symmetry group $Z_9$ with the extension of Standard Model to include some scalar fields.

We construct the Rarita–Schwinger basis vectors, $U^{\mu }$, spanning the direct product space, $U^{\mu }:=A^{\mu }\otimes u_M$, of a massless four-vector, $A^{\mu }$, with massless Majorana spinors, $u_M$, together with the associated field-strength tensor, ${{𝒯}}^{\mu \nu }:=p^{\mu }{U}^{\nu }-p^{\nu }{U}^{\mu }$. The ${{𝒯}}^{\mu \nu }$ space is reducible and contains one massless subspace of a pure spin-$3/2\in (3/2,0)\oplus (0,3/2)$. We show how to single out the latter in a unique way by acting on ${{𝒯}}^{\mu \nu }$ with an earlier derived momentum independent projector, ${{𝒫}}^{(3/2,0)}$, properly constructed from one of the Casimir operators of the algebra $so(1,3)$ of the homogeneous Lorentz group. In this way, it becomes possible to describe the irreducible massless $(3/2,0)\oplus (0,3/2)$ carrier space by means of the antisymmetric tensor of second rank with Majorana spinor components, defined as ${[w^{(3/2,0)}]}^{\mu \nu }:={[{{𝒫}}^{(3/2,0)}]}^{\mu \nu }{}_{\gamma \delta }{{𝒯}}^{\gamma \delta }$. The conclusion is that the $(3/2,0)\oplus (0,3/2)$ bi-vector spinor field can play the same role with respect to a $U^{\mu }$ gauge field as the bi-vector, $(1,0)\oplus (0,1)$, associated with the electromagnetic field-strength tensor, $F_{\mu \nu }$, plays for the Maxwell gauge field, $A_{\mu }$. Correspondingly, we find the free electromagnetic field equation, $p^{\mu }{F}_{\mu \nu }=0$, is paralleled by the free massless Rarita–Schwinger field equation, $p^{\mu }{[w^{(3/2,0)}]}_{\mu \nu }=0$, supplemented by the additional condition, ${\gamma }^{\mu }{\gamma }^{\nu }{[w^{(3/2,0)}]}_{\mu \nu }=0$, a constraint that invokes the Majorana sector.

We investigate the dipole moments of the tau-neutrino at high-energy and high luminosity at linear electron–positron colliders, such as CLIC or ILC through the analysis of the reaction $e^{+}{e}^{-}\to \nu \bar{\nu }\gamma$ in the framework of the $SU{(4)}_L\times U{(1)}_X$ model. The limits on dipole moment were obtained for integrated luminosity of ${ℒ}=250\text{–}1000{\mathrm{\text{fb}}}^{-1}$ and mass ranging from 0.25 to 1.0 TeV. The estimated limits for the tau-neutrino magnetic and electric dipole moments at 95% of confidence level are ${\mu }_{{\nu }_{\tau }}\le 4.83\times 10^{-9}$ and $d_{{\nu }_{\tau }}\le 2.04\times 10^{-19}$ improved by 2–3 orders of magnitude compared to L3 and complement previous studies on the dipole moments.

The motivation behind this study is to enumerate the leading order corrections to the thermodynamics of BTZ black hole (named after three scientists; Banados, Teitelboim, and Zanelli). We first analyze the effect of quantum corrections (motivated from string theory and loop quantum gravity) on various thermodynamic variables for uncharged and stationary BTZ black hole. We, later on, endow charges and rotations to the same black hole and rederive all the expressions once again. The comparative analysis is done between the corrected and uncorrected thermodynamics via plots.

We analyze the structure of the eigenvalue of the color-singlet Balitsky–Fadin–Kuraev–Lipatov (BFKL) equation in N=4 SYM in terms of the meromorphic functions obtained by the analytic continuation of harmonic sums from positive even integer values of the argument to the complex plane. The meromorphic functions we discuss have pole singularities at negative integers and take finite values at all other points. We derive the reflection identities for harmonic sums at weight five decomposing a product of two harmonic sums with mixed pole structure into a linear combination of terms each having a pole at either negative or non-negative values of the argument. The pole decomposition demonstrates how the product of two simpler harmonic sums can build more complicated harmonic sums at higher weight. We list a minimal irreducible set of bilinear reflection identities at weight five which presents the main result of the paper. We show how the reflection identities can be used to restore the functional form of the next-to-leading eigenvalue of the color-singlet BFKL equation in N=4SYM, i.e. we argue that it is possible to restore the full functional form on the entire complex plane provided one has information how the function looks like on just two lines on the complex plane. Finally we discuss how nonlinear reflection identities can be constructed from our result with the use of well known quasi-shuffle relations for harmonic sums.

We discuss an extended model with chiral tensor particles in the Universe. Their direct influence on the Universe dynamics and their characteristic interactions in the hot Universe plasma, considered in the previous publications, are briefly reviewed. A short discussion on the contemporary cosmological bounds on effective number of the relativistic degrees of freedom is provided. Cosmological constraints on the tensor particles interactions strength are obtained, corresponding to different cosmological bounds on the relativistic degrees of freedom and for different assumptions about right-handed neutrinos.