Affine 7-brane Backgrounds and Five-Dimensional $E_N$ Theories on $S^1$

Details Affine 7-brane Backgrounds and Five-Dimensional $E_N$ Theories on $S^1$ Affine 7-brane Backgrounds and Five-Dimensional $E_N$ Theories on $S^1$

1999-07-16

arxiv.org/abs/hep-th/9907134v2

Nucl.Phys.B566:642-660,2000

Physics

High Energy Physics

High Energy Physics - Theory

23 pages, Latex, no figures, some statements clarified, typos corrected, references and note added

Scientific paper

10.1016/S0550-3213(99)00634-3

Elliptic curves for the 7-brane configurations realizing the affine Lie algebras $\wh E_n$ $(1 \leq n \leq 8)$ and $\wh{\wt E}_n$ $(n=0,1)$ are systematically derived from the cubic equation for a rational elliptic surface. It is then shown that the $\wh E_n$ 7-branes describe the discriminant locus of the elliptic curves for five-dimensional (5D) N=1 $E_n$ theories compactified on a circle. This is in accordance with a recent construction of 5D N=1 $E_n$ theories on the IIB 5-brane web with 7-branes, and indicates the validity of the D3 probe picture for 5D $E_n$ theories on $\bR^4 \times S^1$. Using the $\wh E_n$ curves we also study the compactification of 5D $E_n$ theories to four dimensions.

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