Dualities and the SL(2,Z) Anomaly

TL;DR

This paper explains the SL(2,Z) anomaly in type IIB supergravity as a consequence of T-duality with type IIA string theory after compactification, revealing deep connections between dualities, anomalies, and effective actions in string theory.

Contribution

It demonstrates that the SL(2,Z) anomaly arises from T-duality relations between type IIA and IIB theories upon compactification, linking anomalies to duality symmetries and effective action identities.

Findings

SL(2,Z) anomaly linked to T-duality in compactified theories

Constraints on compactification manifolds from modular invariance

Presence of similar anomalies on M-theory 5-branes and orientifold 5-planes

Abstract

The SL(2,Z) anomaly recently derived for type IIB supergravity in 10 dimensions is shown to be a consequence of T-duality with the type IIA string, after compactification to 2 dimensions on an 8-fold. This explains the identity of the gravitational 8-forms appearing in different contexts in the effective actions of type IIA and IIB string theories. In this framework, constraints on the compactification manifold arise from modular invariance of the 2d theory. Related issues in 6 dimensions are examined, and it is argued that similar anomalies are present on the worldvolumes of M-theory 5-branes and orientifold 5-planes.