T-Duality, and the K-Theoretic Partition Function of TypeIIA Superstring Theory

TL;DR

This paper investigates the T-duality invariance of the type IIA string theory partition function on specific 10-manifolds, emphasizing topological phases, anomalies, and quantum corrections, with implications for M-theory and U-duality.

Contribution

It demonstrates the necessity of including anomalies and quantum corrections to achieve T-duality invariance in the partition function of type IIA string theory.

Findings

Partition function is T-duality invariant when anomalies and quantum effects are included.

Topological phases from K-theory are crucial for consistency.

Implications for M-theory and U-duality are discussed.

Abstract

We study the partition function of type IIA string theory on 10-manifolds of the form T^2 x X where X is 8-dimensional, compact, and spin. We pay particular attention to the effects of the topological phases in the supergravity action implied by the K-theoretic formulation of RR fields, and we use these to check the T-duality invariance of the partition function. We find that the partition function is only T-duality invariant when we take into account the T-duality anomalies in the RR sector, the fermionic path integral (including 4-fermi interaction terms), and 1-loop corrections including worldsheet instantons. We comment on applications of our computation to speculations about the role of the Romans mass in M-theory. We also discuss some issues which arise when one attempts to extend these considerations to checking the full U-duality invariance of the theory.