Eleven Dimensional Origin of String/String Duality: A One Loop Test

TL;DR

Duff, Liu, and Minasian test the conjectured eleven-dimensional origin of string/string duality by deriving the $D=10$ Type IIA and $D=6$ heterotic Bianchi identities from the Chern-Simons corrections to the $D=11$ fivebrane Bianchi identities and their $K3$-compactifications. They show that the $D=10$ Lorentz/gauge Chern-Simons terms and the $D=6$ Narain-structure of abelian fields emerge consistently, providing a unified framework in which membrane/fivebrane duality explains Type IIA/heterotic duality across dimensions. By exploiting the absence of a dilaton in $D=11$, they fix both the gravitational constant and the fivebrane tension in terms of the membrane tension and relate tensions via Dirac quantization, while addressing the elementary vs solitonic heterotic string issue and exploring potential fivebrane origins of S-duality. Collectively, the work reinforces the view that eleven dimensions and super p-branes organize string dualities and illuminate the deep connections among M-theory objects, Type II strings, and heterotic strings.

Abstract

Membrane/fivebrane duality in D=11 implies Type IIA string/Type IIA fivebrane duality in D=10, which in turn implies Type IIA string/heterotic string duality in D=6. To test the conjecture, we reproduce the corrections to the 3-form field equations of the D=10 Type IIA string (a mixture of tree-level and one-loop effects) starting from the Chern-Simons corrections to the 7-form Bianchi identities of the D=11 fivebrane (a purely tree-level effect). K3 compactification of the latter then yields the familiar gauge and Lorentz Chern-Simons corrections to 3-form Bianchi identities of the heterotic string. We note that the absence of a dilaton in the D=11 theory allows us to fix both the gravitational constant and the fivebrane tension in terms of the membrane tension. We also comment on an apparent conflict between fundamental and solitonic heterotic strings and on the puzzle of a fivebrane origin of S-duality.

Figures (3)

• Figure 1: Compactifications relating $(a)$ the Type $IIA$ fivebrane to the heterotic string and $(b)$ the heterotic fivebrane to the Type $IIA$ string. Worldvolume supersymmetries are indicated.
• Figure 2: Compactifications incorporating worldvolume reductions.
• Figure 3: A superposition of Figs. 1 $(a)$ and $(b)$, illustrating strong/weak coupling dualities (denoted by the dotted lines).