Duality of Type II 7-branes and 8-branes

TL;DR

This paper explores the duality between Type II 7-branes and 8-branes, introducing a new massive supergravity theory and revealing implications for the cosmological constant through T-duality and U-duality symmetries.

Contribution

It presents a new massive N=2 D=9 supergravity theory and establishes dualities linking 7-branes and 8-branes, with implications for string theory cosmology.

Findings

Constructed a multi 8-brane solution generalizing Polchinski and Witten's 8-brane.

Demonstrated T-duality between 8-branes and 7-branes in compactified IIB supergravity.

Implication of quantized cosmological constant in type IIA string theory.

Abstract

We present a version of ten-dimensional IIA supergravity containing a 9-form potential for which the field equations are equivalent to those of the standard, massless, IIA theory for vanishing 10-form field strength, $F_{10}$, and to those of the `massive' IIA theory for non-vanishing $F_{10}$. We present a multi 8-brane solution of these equations that generalizes the 8-brane of Polchinski and Witten. We show that this solution is T-dual to a new multi 7-brane solution of $S^1$ compactified IIB supergravity, and that the latter is T-dual to the IIA 6-brane. When combined with the $Sl(2;\Z)$ U-duality of the type IIB superstring, the T-duality between type II 7-branes and 8-branes implies a quantization of the cosmological constant of type IIA superstring theory. These results are made possible by the construction of a new {\it massive} N=2 D=9 supergravity theory. We also discuss the 11-dimensional interpretation of these type II p-branes.