International Journal of Modern Physics A

Through a self-dual mapping of the geometry AdS₅ ×S⁵, fermionic T-duality provides a beautiful geometric interpretation of hidden symmetries for scattering amplitudes in super-Yang–Mills. Starting with Green–Schwarz sigma-models, we consolidate developments in this area into this small review. In particular, we discuss the translation of fermionic T-duality into the supergravity fields via pure spinor formalism and show that a general class of fermionic transformations can be identified directly in the supergravity. In addition to discussing fermionic T-duality for the geometry AdS₄ × ℂP³, dual to ABJM theory, we review work on other self-dual geometries. Finally, we present a short round-up of studies with a formal interest in fermionic T-duality.

We consider the one-loop effective potential at zero temperature in Lifshitz-type field theories with anisotropic space–time scaling, with critical exponent z = 3, including scalar, fermion and gauge fields. The fermion determinant generates a symmetry breaking term at one loop in the effective potential and a local minimum appears, for nonzero scalar field, for every value of the Yukawa coupling. Depending on the relative strength of the coupling constants for the scalar and the gauge field, we find a second symmetry breaking local minimum in the effective potential for a bigger value of the scalar field.

Solutions to the Dirac equation are constructed for a massless charged fermion in Coulomb and Aharonov–Bohm (AB) potentials in 2+1 dimensions. The Dirac Hamiltonian on this background is singular and needs a one-parameter self-adjoint extension, which can be given in terms of self-adjoint boundary conditions. We show that the virtual (quasistationary) bound states emerge in the presence of an attractive Coulomb potential when the so-called effective charges become overcritical and discuss a restructuring of the vacuum of the quantum electrodynamics when the virtual bound states emerge. We derive equations, which determine the energies and lifetimes of virtual bound states, find solutions of obtained equations for some values of parameters as well as analyze the local density of states (LDOS) as a function of energy in the presence of Coulomb and AB potentials.

Dynamics of π, K-mesons interactions is formulated in terms of composite superconformal string model. Supersymmetry is defined on two-dimensional world surface only. Dimensionality of target space equals to four. The model treats usual hadron scale which is of order 1 GeV^-2, as string scale α′. Intercept of leading meson trajectory equals to ½. Tree amplitudes are free from ghosts in physical state spectrum in accordance with usual classical superstring amplitudes. Interaction of π-mesons in the chiral limit in the model turns out in correspondence with description in terms of chiral Lagrangian for pions in QCD.

According to the conjecture of the gauge/gravity duality, a strongly coupled 4D field theory may be described by a dual 5D theory which is a free field theory in the first approximation. The usual description of the axial-vector sector in the bottom–up AdS/QCD models includes, however, the quartic interaction with a bulk scalar field. A question arises, whether it is possible to describe some aspects of the chiral symmetry breaking (CSB) in a way more consistent with the original proposal, i.e. within a free 5D theory? We suggest that a natural candidate for this purpose is the soft wall (SW) model with inverse exponential profile.

We study the production of the lightest neutralinos in the radiative process in supersymmetric models with grand unification. We consider models wherein the standard model (SM) gauge group SU(3)_c ×SU(2)_L ×U(1)_Y is unified into the grand unified gauge groups SU(5) or SO(10). We study this process at energies that may be accessible at a future International Linear Collider (ILC). We compare and contrast the dependence of the signal cross-section on the grand unified gauge group, and different representations of the grand unified gauge group, into which the SM gauge group is unified. We carry out a comprehensive study of the radiative production process which includes higher-order QED corrections in our calculations. In addition we carry out a detailed study of the background to the signal process coming from the SM radiative neutrino production , as well as from the radiative production of the scalar partners of the neutrinos (sneutrinos) . The latter can be a major supersymmetric background to the radiative production of neutralinos when the sneutrinos decay invisibly. It is likely that the radiative production of the lightest neutralinos may be a viable channel to study supersymmetric partners of the SM particles at the first stage of an ILC, where heavier sparticles may be too heavy to be produced in pairs.

Recent efforts to classify representations of supersymmetry with no central charge [C. F. Doran et al., Adv. Theor. Math. Phys.15, 1909 (2011)] have focused on supermultiplets that are aptly depicted by Adinkras, wherein every supersymmetry generator transforms each component field into precisely one other component field or its derivative. Herein, we study gauge-quotients of direct sums of Adinkras by a supersymmetric image of another Adinkra and thus solve a puzzle in the paper by Doran et al., Int. J. Mod. Phys. A22, 869 (2007): such (gauge-)quotients are not Adinkras but more general types of supermultiplets, each depicted as a connected network of Adinkras. Iterating this gauge-quotient construction then yields an indefinite sequence of ever larger supermultiplets, reminiscent of Weyl's construction that is known to produce all finite-dimensional unitary representations in Lie algebras.