Four-dimensional vector multiplets in arbitrary signature (II)

Following the classification up to isomorphism of [Formula: see text] Poincaré Lie superalgebras in four dimensions with arbitrary signature obtained in a companion paper, we present off-shell vector multiplet representations and invariant Lagrangians realizing these algebras. By dimensional reduction of five-dimensional off-shell vector multiplets, we obtain two representations in each four-dimensional signature. In Euclidean and neutral signature, these representations can be mapped to each other by a field redefinition induced by the action of the Schur group on the space of superbrackets. In Minkowski signature, we show that the superbrackets underlying the two vector multiplet representations belong to distinct open orbits of the Schur group and are therefore inequivalent. Our formalism allows to answer questions about the possible relative signs between terms in the Lagrangian systematically by relating them to the underlying space of superbrackets.

Pseudo-Riemannian universe from Euclidean bulk

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 [Formula: see text]. It is shown that stability of brane vibrations requires [Formula: see text]. 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 [Formula: see text]. 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.

BOUNCES/DYONS IN THE PLANE WAVE MATRIX MODEL AND SU(N) YANG–MILLS THEORY

We consider SU (N) Yang–Mills theory on the space ℝ × S3 with Minkowski signature (-+++). The condition of SO(4)-invariance imposed on gauge fields yields a bosonic matrix model which is a consistent truncation of the plane wave matrix model. For matrices parametrized by a scalar ϕ, the Yang–Mills equations are reduced to the equation of a particle moving in the double-well potential. The classical solution is a bounce, i.e. a particle which begins at the saddle point ϕ = 0 of the potential, bounces off the potential wall and returns to ϕ = 0. The gauge field tensor components parametrized by ϕ are smooth and for finite time, both electric and magnetic fields are nonvanishing. The energy density of this non-Abelian dyon configuration does not depend on coordinates of ℝ × S3 and the total energy is proportional to the inverse radius of S3. We also describe similar bounce dyon solutions in SU (N) Yang–Mills theory on the space ℝ × S2 with signature (-++). Their energy is proportional to the square of the inverse radius of S2. From the viewpoint of Yang–Mills theory on ℝ1,1 × S2 these solutions describe non-Abelian (dyonic) flux tubes extended along the x3-axis.

CT-DUALITY AS A LOCAL PROPERTY OF THE WORLDSHEET

In this present article, we study the local features of the worldsheet in the case when probe bosonic string moves in antisymmetric background field. We generalize the geometry of surfaces embedded in spacetime to the case when the torsion is present. We define the mean extrinsic curvature for spaces with Minkowski signature and introduce the concept of mean torsion. Its orthogonal projection defines the dual mean extrinsic curvature. In this language, the field equation is just the equality of mean extrinsic curvature and extrinsic mean torsion, which we call CT-duality. To the worldsheet described by this relation we will refer as CT-dual surface.

RIGID QED AND NONLINEAR SIGMA MODELS

We show that in the absence of Coulomb interactions the kinetic theory of a recently proposed new model of strongly coupled QED behaves like an enhanced two-dimensional nonlinear sigma model with O(D+1) symmetry in Euclidean signature (which becomes an on-compact O(D, 1) symmetry in Minkowski signature). The beta-function is nontrivial in the absence of virtual fermions due to the non-perturbative vacuum fluctuation of the gauge field. In the presence of Coulomb the running coupling approaches an uv stable fixed point αc of order one. In the weak phase the curvature coupling increases at short distances and decreases at large distances.