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.

On Clifford-algebraic dimensional extension and SUSY holography

We analyze the group of maximal automorphisms of the N-extended worldline supersymmetry algebra, and its action on off-shell supermultiplets. This defines a concept of "holoraumy" that extends the notions of holonomy and curvature in a novel way and provides information about the geometry of the supermultiplet field-space. In turn, the "holoraumy" transformations of 0-brane dimensionally reduced supermultiplets provide information about Lorentz transformations in the higher-dimensional space–time from which the 0-brane supermultiplets are descended. Specifically, Spin(3) generators are encoded within 0-brane "holoraumy" tensors. Worldline supermultiplets are thus able to holographically encrypt information about higher-dimensional space–time geometry.

A supersymmetric Lagrangian for fermionic fields with mass dimension one

We present the derivation of a supersymmetric model for fermionic fields with integer-valued mass dimension based on a general superfield with one free spinor index. First, we develop a formalism based on a general superfield with one free spinor index. Then, we systematically derive all associated chiral and antichiral superfields up to third order in covariant derivatives. Using this formalism we are able to construct a supersymmetric on-shell Lagrangian that contains a kinetic term for the fermionic fields with mass dimension one. We then derive the corresponding on-shell supercurrent and succeed in formulating a consistent second quantization for the component fields. Finally, we present our result for a supersymmetric Hamiltonian. As the Lagrangian is by construction supersymmetric and the Hamiltonian was derived from the Lagrangian using supersymmetry algebra the Hamiltonian must be positive definite.