T-Duality of p-Branes

TL;DR

This paper explores a duality symmetry, specifically SL(2,Z), that exchanges Kaluza-Klein modes with wrapping modes of p-branes on tori, within the framework of string theory and M-theory, revealing a new aspect of p-brane dualities.

Contribution

It demonstrates the existence of an SL(2,Z) duality symmetry for BPS p-branes that interchanges Kaluza-Klein and wrapping modes on a torus, based on conjectured U-duality symmetries.

Findings

Identifies an SL(2,Z) symmetry mixing modes of p-branes on tori.

Shows the modular parameter relates to gauge field components and torus volume.

Supports the conjecture of duality symmetries in string and M-theory contexts.

Abstract

We investigate possible existence of duality symmetries which exchange the Kaluza-Klein modes with the wrapping modes of a BPS saturated $p$-brane on a torus. Assuming the validity of the conjectured $U$-duality symmetries of type II and heterotic string theories and $M$-theory, we show that for a BPS saturated $p$-brane there is an SL(2,Z) symmetry that mixes the Kaluza-Klein modes on a $(p+1)$ dimensional torus $T^{(p+1)}$ with the wrapping modes of the $p$-brane on $T^{(p+1)}$. The field that transforms as a modular parameter under this SL(2,Z) transformation has as its real part the component of the $(p+1)$-form gauge field on $T^{(p+1)}$, and as its imaginary part the volume of $T^{(p+1)}$, measured in the metric that couples naturally to the $p$-brane.