Unification of massless field equations solutions for any spin

A unification in terms of exact solutions for massless Klein–Gordon, Dirac, Maxwell, Rarita– Schwinger, Einstein, and bosonic and fermionic fields of any spin is presented. The method is based on writing all of the relevant dynamical fields in terms of products and derivatives of pre–potential functions, which satisfy d’Alambert equation. The coupled equations satisfied by the pre–potentials are non-linear. Remarkably, there are particular solutions of (gradient) orthogonal pre–potentials that satisfy the usual wave equation which may be used to construct exact non–trivial solutions to Klein–Gordon, Dirac, Maxwell, Rarita–Schwinger, (linearized and full) Einstein and any spin bosonic and fermionic field equations, thus giving rise to an unification of the solutions of all massless field equations for any spin. Some solutions written in terms of orthogonal pre–potentials are presented. Relations of this method to previously developed ones, as well as to other subjects in physics are pointed out.

Generalized F(R, T) cosmological models with fermionic fields

We investigated the gravity model F (R, T), which interacts with a fermion field in a uniform and isotropic at spacetime FLRW. The main idea and purpose of the work donewas to create a mathematical model and find a particular solution for the scale factor a, since it describes the dynamics of the evolution of the Universe. The solutions for this universe are obtained using the Noether symmetry method. With its help, a specific form of the Lagrangian is obtained. And the possible types of the scale factor were found. The evolution of the resulting cosmological model has been investigated.

On the abundance of supersymmetric strings in AdS 3 x S 3 x S 3 x S 1 describing BPS line operators

We study supersymmetric open strings in type IIB $AdS_3 \times S^3 \times S^3 \times S^1$ with mixed R-R and NS-NS fields. We focus on strings ending along a straight line at the boundary of $AdS_3$, which can be interpreted as line operators in a dual CFT$_2$. We study both classical configurations and quadratic fluctuations around them. We find that strings sitting at a fixed point in $S^3 \times S^3 \times S^1$, i.e. satisfying Dirichlet boundary conditions, are 1/2 BPS. We also show that strings sitting at different points of certain submanifolds of $S^3 \times S^3 \times S^1$ can still share some fraction of the supersymmetry. This allows to define supersymmetric smeared configurations by the superposition of them, which range from 1/2 BPS to 1/8 BPS. In addition to the smeared configurations, there are as well 1/4 BPS and 1/8 BPS strings satisfying Neumann boundary conditions. All these supersymmetric strings are shown to be connected by a network of interpolating BPS boundary conditions. Our study reveals the existence of a rich moduli of supersymmetric open string configurations, for which the appearance of massless fermionic fields in the spectrum of quadratic fluctuations is crucial.

Supersymmetry, T-duality and heterotic α′-corrections

Higher-derivative interactions and transformation rules of the fields in the effective field theories of the massless string states are strongly constrained by space-time symmetries and dualities. Here we use an exact formulation of ten dimensional $$ \mathcal{N} $$ N = 1 supergravity coupled to Yang-Mills with manifest T-duality symmetry to construct the first order α′-corrections of the heterotic string effective action. The theory contains a supersymmetric and T-duality covariant generalization of the Green-Schwarz mechanism that determines the modifications to the leading order supersymmetry transformation rules of the fields. We compute the resulting field-dependent deformations of the coefficients in the supersymmetry algebra and construct the invariant action, with up to and including four-derivative terms of all the massless bosonic and fermionic fields of the heterotic string spectrum.

Effective theories and non-minimal couplings in low-dimensional systems

Dimensionality aspects of non-minimal electromagnetic couplings are investigated. By means of the Foldy–Wouthuysen transformation, we attain (non-)relativistic interactions related to the non-minimal coupling in three-dimensional spacetime, for both the bosonic and fermionic fields. Next, we establish some comparisons and analyze particular situations in which the external electromagnetic fields are described either by Maxwell or Maxwell–Chern–Simons Electrodynamics. In addition, we consider the situation of a non-minimal coupling for the fermionic field in four dimensions, carry out its dimensional reduction to three dimensions and show that the three-dimensional scenario previously worked out can be recovered as a particular case. Finally, we discuss a number of structural aspects of both procedures.

Influence of Fermions on Vortices in SU(2)-QCD

Gauge fields control the dynamics of fermions, also a back reaction of fermions on the gauge field is expected. This back reaction is investigated within the vortex picture of the QCD vacuum. We show that the center vortex model reproduces the string tension of the full theory also with the presence of fermionic fields.

$$ \mathcal{N} $$ = 2 AdS4 supergravity, holography and Ward identities

We develop in detail the holographic framework for an $$ \mathcal{N} $$ N = 2 pure AdS supergravity model in four dimensions, including all the contributions from the fermionic fields and adopting the Fefferman-Graham parametrization. We work in the first order formalism, where the full superconformal structure can be kept manifest in principle, even if only a part of it is realized as a symmetry on the boundary, while the remainder has a non-linear realization. Our study generalizes the results presented in antecedent literature and includes a general discussion of the gauge-fixing conditions on the bulk fields which yield the asymptotic symmetries at the boundary. We construct the corresponding super- conformal currents and show that they satisfy the related Ward identities when the bulk equations of motion are imposed. Consistency of the holographic setup requires the super- AdS curvatures to vanish at the boundary. This determines, in particular, the expression of the super-Schouten tensor of the boundary theory, which generalizes the purely bosonic Schouten tensor of standard gravity by including gravitini bilinears. The same applies to the superpartner of the super-Schouten tensor, the conformino. Furthermore, the vanishing of the supertorsion poses general constraints on the sources of the three-dimensional boundary conformal field theory and requires that the super-Schouten tensor is endowed with an antisymmetric part proportional to a gravitino-squared term.

Exactly solvable single-trace four point correlators in χCFT4

In this paper we study a wide class of planar single-trace four point correlators in the chiral conformal field theory (χCFT4) arising as a double scaling limit of the γ-deformed $$ \mathcal{N} $$ N = 4 SYM theory. In the planar (t’Hooft) limit, each of such correlators is described by a single Feynman integral having the bulk topology of a square lattice “fishnet” and/or of an honeycomb lattice of Yukawa vertices. The computation of this class of Feynmann integrals at any loop is achieved by means of an exactly-solvable spin chain magnet with SO(1, 5) symmetry. In this paper we explain in detail the solution of the magnet model as presented in our recent letter and we obtain a general formula for the representation of the Feynman integrals over the spectrum of the separated variables of the magnet, for any number of scalar and fermionic fields in the corresponding correlator. For the particular choice of scalar fields only, our formula reproduces the conjecture of B. Basso and L. Dixon for the fishnet integrals.