Relatively and supersymmetries

We show how the supersymmetry transformations follow from the relativization of a pseudoclassical lagrangian describing particles with spin.     

Superspaces and supersymmetries

A theory of graded Banach modules over a Banach-Grassmann algebra is developed and applied to differential geometry of super-manifolds. The explicit structure of superspaces carrying Poincaré supersymmetry and extended supersymmetry, including central charges, is described.     

Modified supersymmetries

An attempt is made to modify super-symmetry groups and the algebra of the underlying elements, so that the mappings involved in the realizations are those of an ordinary manifold on itself. The resulting group possesses representations that transform constant tensors and spinors among each other. Applications to fiber bundles lead to fields over general space-time manifolds whose structure group is the modified super-symmetry group.Supported by National Science Foundation Grant No. MPS74-15246.     

Generalized contact geometry and T-duality

We study generalized almost contact structures on odd-dimensional manifolds. We introduce a notion of integrability and show that the class of these structures is closed under symmetries of the Courant–Dorfman bracket, including T-duality. We define a notion of geometric type for generalized almost contact structures, and study its behavior under T-duality.     

Fibre bundles and supersymmetries

By extending the frame bundle of a manifold admitting a spin structure to a principal fibre bundle with group the super-Poincaré group we are able to derive the supergravity Lagrangian and its invariances under supersymmetry and other transformations in a global form.     

Connecting T-duality invariant theories

We show that the vanishing of the one-loop beta-functional of the doubled formalism (which describes string theory on a torus fibration in which the fibres are doubled) is the same as the equation of motion of the recently proposed generalised metric formulation of double field theory restricted to this background: both are the vanishing of a generalised Ricci tensor. That this tensor arises in both backgrounds indicates the importance of a new doubled differential geometry for understanding both constructions.     

Poisson-Lie T-duality and Bianchi type algebras

All Bianchi bialgebras have been obtained. By introducing a non-degenerate adjoint invariant inner product over these bialgebras the associated Drinfeld doubles have been constructed, then by calculating the coupling matrices for these bialgebras several σ-models with Poisson-Lie symmetry have been obtained. Two simple examples as prototypes of Poisson-Lie dual models have been given.     

Broken supersymmetries and shifted superpropagators

Superfield Feynman rules are derived for a general case where global supersymmetry is spontaneously broken by F-terms. The complete superspace dependence of the superpropagators is factored out and they are employed to discuss the corrections to the effective action and the non-renormalisation theorems. Their coupling to external gauge superfields is also contemplated and finite matter contributions to the gaugino mass and the Fayet-Iliopoulos term are considered.     

Quantum extended supersymmetries

We analyse some quantum multiplets associated with extended supersymmetries. We study in detail the general form of the causal (anti)commutation relations. The condition of positivity of the scalar product imposes severe restrictions on the (quantum) model. It is problematic if one can find out quantum extensions of the standard model with extended supersymmetries.     

S-matrix elements from T-duality

Recently it has been speculated that the S-matrix elements satisfy the Ward identity associated with the T-duality. This indicates that a group of S-matrix elements is invariant under the linear T-duality transformations on the external states. If one evaluates one component of such T-dual multiplet, then all other components may be found by the simple use of the linear T-duality. The assumption that fields must be independent of the Killing coordinate, however, may cause, in some cases, the T-dual multiplet not to be gauge invariant. In those cases, the S-matrix elements contain more than one T-dual multiplet which are intertwined by the gauge symmetry.     

Some remarks on defects and T-duality

The equations of motion for a conformal field theory in the presence of defect lines can be derived from an action that includes contributions from bibranes. For T-dual toroidal compactifications, they imply a direct relation between Poincaré line bundles and the action of T-duality on boundary conditions. We also exhibit a class of diagonal defects that induce a shift of the B-field. We finally study T-dualities for S¹$S^1$-fibrations in the example of the Wess–Zumino–Witten model on SU(2)$\mathrm{SU}(2)$ and lens spaces. Using standard techniques from D-branes, we derive from algebraic data in rational conformal field theories geometric structures familiar from Fourier–Mukai transformations.     

High spin limits and non-abelian T-duality

The action of the non-abelian T-dual of the WZW model is related to an appropriate gauged WZW action via a limiting procedure. We extend this type of equivalence to other σ-models with non-abelian isometries and their non-abelian T-duals, focusing on Principal Chiral models. We reinforce and refine this equivalence by arguing that the non-abelian T-duals are the effective backgrounds describing states of an appropriate parent theory corresponding to divergently large highest weight representations. The proof involves carrying out a subtle limiting procedure in the group representations and relating them to appropriate limits in the corresponding backgrounds. We illustrate the general method by providing several non-trivial examples.     

Entropy of black-branes system and T-duality

A general black-branes system under the T-duality transformation could produce a smeared system with different dimensional black branes. We first use some simple examples to see that both systems have the same entropy and then present a rigorous method to prove this general property. Using the property we could easily know the entropy of some complex black-brane systems.     

On nature of supersymmetries

The problem of emergence of supersymmetry is considered. It is argued that putting of a set of harmonic oscillators into a thermal bath gives both quantum mechanics and supersymmetric structures.     

Extended supersymmetries and the Dirac operator

We consider supersymmetric quantum mechanical systems in arbitrary dimensions on curved spaces with nontrivial gauge fields. The square of the Dirac operator serves as Hamiltonian. We derive a relation between the number of supercharges that exist and restrictions on the geometry of the underlying spaces as well as the admissible gauge field configurations. From the superalgebra with two or more real supercharges we infer the existence of integrability conditions and obtain a corresponding superpotential. This potential can be used to deform the supercharges and to determine zero modes of the Dirac operator. The general results are applied to the Kähler spaces CPⁿ.