Abstract
It is well understood — through string dualities — that there are 20 massless vector fields in the spectrum of eight-dimensional F-theory compactifications on smooth elliptically fibered K3 surfaces at a generic point in the K3 moduli space. Such F-theory vacua, which do not have any enhanced gauge symmetries, can be thought of as supersymmetric type IIB compactifications on \( \mathbb{P} \) 1 with 24 (p, q) seven-branes. Naively, one might expect there to be 24 massless vector fields in the eight-dimensional effective theory coming from world-volume gauge fields of the 24 branes. In this paper, we show how the vector field spectrum of the eight-dimensional effective theory can be obtained from the point of view of type IIB supergravity coupled to the world-volume theory of the seven-branes. In particular, we first show that the two-forms of the type IIB theory absorb the seven-brane world-volume gauge fields via the Cremmer-Scherk mechanism. We then proceed to show that the massless vector fields of the eight-dimensional theory come from KK-reducing the SL(2, \( \mathbb{Z} \)) doublet two-forms of type IIB theory along SL(2, \( \mathbb{Z} \)) doublet one-forms on the \( \mathbb{P} \) 1. We also discuss the relation between these vector fields and the “eaten” world-volume vector fields of the seven-branes.
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Douglas, M.R., Park, D.S. & Schnell, C. The Cremmer-Scherk mechanism in F-theory compactifications on K3 manifolds. J. High Energ. Phys. 2014, 135 (2014). https://doi.org/10.1007/JHEP05(2014)135
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DOI: https://doi.org/10.1007/JHEP05(2014)135