Duality Covariant Type IIB Supersymmetry and Nonperturbative Consequences

TL;DR

This paper develops a superalgebra framework for type IIB string theory that incorporates SL(2,Z) duality, enabling non-perturbative calculations of string tensions, black hole properties, and suggesting a higher-dimensional fundamental theory.

Contribution

It introduces a moduli-dependent superalgebra formalism that captures non-perturbative duality effects and extends the understanding of type IIB supersymmetry beyond perturbation theory.

Findings

Computed the tension of (p,q) strings algebraically.

Calculated the mass and entropy of extremal black holes from D-branes.

First non-perturbative coupling dependence of BPS mass and metric.

Abstract

Type-IIB supersymmetric theories have an SL(2,Z) invariance, known as U-duality, which controls the non-perturbative behavior of the theory. Under SL(2,Z) the supercharges are doublets, implying that the bosonic charges would be singlets or triplets. However, among the bosonic charges there are doublet strings and doublet fivebranes which are in conflict with the doublet property of the supercharges. It is shown that the conflict is resolved by structure constants that depend on moduli, such as the tau parameter, which transform under the same SL(2,Z). The resulting superalgebra encodes the non-perturbative duality properties of the theory and is valid for any value of the string coupling constant. The usefulness of the formalism is illustrated by applying it to purely algebraic computations of the tension of (p,q) strings, and the mass and entropy of extremal blackholes constructed from D-1-branes and D-5-branes. In the latter case the non-perturbative coupling dependence of the BPS mass and metric is computed for the first time in this paper. It is further argued that the moduli dependence of the superalgebra provides hints for four more dimensions beyond ten, such that the superalgebra is embedded in a fundamental theory which would be covariant under SO(11,3). An outline is given for a matrix theory in 14 dimensions that would be consistent with M(atrix) theory as well as with the above observations.