SO(2,1) Covariant IIB Superalgebra

TL;DR

This paper introduces a new SO(2,1) covariant superalgebra for type IIB superstring theory, providing a geometric framework that explains SL(2,R) duality and U(1) fields.

Contribution

It proposes a novel super-Poincare algebra with SO(2,1) covariance and constructs a coset model that captures the SL(2,R) duality and U(1) gauge fields in IIB superstring theory.

Findings

The algebra incorporates SO(2,1) and SO(9,1) generators with a triplet of momenta.

The coset construction yields the SL(2,R) 2-form doublet.

U(1) connections are identified as coordinates of an enlarged space.

Abstract

We propose a type IIB super-Poincare algebra with SO(2,1) covariant central extension. Together with SO(2,1) and SO(9,1) generators, a SO(2,1) triplet (momenta), a Majorana-spinor doublet (supercharges) and a Rarita-Schwinger central charge generate a group, G. We consider a coset G/H where H=(SO(2) x Lorentz), and the SL(2,R) 2-form doublet is obtained by the coset construction. It is shown that U(1) connections, whose strengths are associated with 2-forms, are recognized as coordinates of the enlarged space. We suggest that this is the fundamental algebra governing the superstring theories which explains the IIB SL(2,R) duality and geometrical origin of U(1) fields.