Abstract
We investigate the field dependence of the gauge coupling functions of four-dimensional Type IIB orientifold and F-theory compactifications with space-time filling seven-branes. In particular, we analyze the constraints imposed by holomorphicity and covariance under shift-symmetries of the bulk and brane axions. This requires introducing quantum corrections that necessarily contain Riemann theta functions on the complex torus spanned by the D7-brane Wilson line moduli. Our findings hint towards a new underlying geometric structure for gauge coupling functions in string compactifications. We generalize this discussion to a genuine F-theory compactification on an elliptically fibered Calabi-Yau fourfold. We perform the first general dimensional reduction of eleven-dimensional super-gravity and dualization to the F-theory frame. The resulting effective action is compared with the circle reduction of a four-dimensional mathcal{N} = 1 supergravity theory. The F-theory geometry elegantly unifies bulk and brane degrees of freedom and allows us to infer non-trivial results about holomorphicity and shift-symmetries. For instance, we gain new insight into kinetic mixing of bulk and brane gauge fields.
Highlights
Only receives perturbative corrections to one-loop order, while non-perturbative corrections can be generally present
We investigate the field dependence of the gauge coupling functions of fourdimensional Type IIB orientifold and F-theory compactifications with space-time filling seven-branes
In effective theories arising from string theory, the gauge coupling function can depend on scalars admitting classical shift-symmetries
Summary
We consider the four-dimensional effective action that arises from Calabi-Yau orientifold compactifications of Type IIB with D7-branes and O7-planes. We aim to determine the characteristic functions determining the standard N = 1 supergravity with bosonic action [1]. Where KABs are the second derivatives of a real Kahler potential K (M , MĎ ) and fIJ(M ) is the holomorphic gauge coupling function. We will denote four-dimensional quantities with a hat. The functions K , fIJ as well as the complex coordinates M A are determined by reducing Type IIB supergravity coupled to the D7-brane and O7-plane world-volume actions following and extending [6, 7, 16]. We will discuss the shift-symmetries and certain quantum corrections of the effective theory
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