Abstract
We introduce a new approach to investigate the selection rules governing the contributions of fluxed M5-instantons to the F-theory four-dimensional effective action, with emphasis on the generation of charged matter F-terms. The structure of such couplings is unraveled by exploiting the perturbative and non-perturbative homological relations, introduced in our companion paper [1], which encode the interplay between the self-dual 3-form flux on the M5-brane, the background 4-form flux and certain fibral curves. The latter are wrapped by time-like M2-branes representing matter insertions in the instanton path integral. In particular, we clarify how fluxed M5-instantons detect the presence of geometrically massive U(1)s which are responsible for ‘hidden’ selection rules. We discuss how for non-generic embeddings the M5-instanton can probe ‘locally massless’ U(1) symmetries if the rank of its Mordell-Weil group is enhanced compared to that of the bulk. As a phenomenological off-spring we propose a new type of non-perturbative corrections to Yukawa couplings which may change the rank of the Yukawa matrix. Along the way, we also gain new insights into the structure of massive U(1) gauge fluxes in the stable degeneration limit.
Highlights
We introduce a new approach to investigate the selection rules governing the contributions of fluxed M5-instantons to the F-theory four-dimensional effective action, with emphasis on the generation of charged matter F-terms
The information relevant for the computation of such operators is encoded already in the classical Bianchi identity of the 3-form field strength T3 associated with the chiral 2-form on the M5-brane. This Bianchi identity describes the interplay between the instanton 3-form flux T3, the gauge flux G4 in the F-theory bulk and further time-like M2-branes that can end on the M5-brane instanton
As we will discuss in some detail in the following, the Bianchi identity (2.10) gives rise to the selection rules that constrain the types of terms a given instanton with flux can generate in the effective action
Summary
In this paper we study D3/M5-instantons on general F-theory compactifications to four dimensions, either admitting a weak coupling limit or not. As we will discuss in some detail in the following, the Bianchi identity (2.10) gives rise to the selection rules that constrain the types of terms a given instanton with flux can generate in the effective action This is already clear by imposing (2.10) just at the cohomological level, i.e. where [G4]D and [C]D denote the cohomology classes of G4|D and of the Poincare dual of C, respectively, inside D. As already observed in [13, 16, 20], this condition allows us to understand the M5-analogue of a D3-instanton in which charged chiral zero modes are induced only by 7-brane worldvolume fluxes In this case, the instanton generates terms which include operators charged under U(1) gauge symmetries that are massive by means of a flux induced Stuckelberg mechanism. If non-vanishing, such torsional contribution should be cancelled by appropriate M2-brane insertions and in the following we assume that such cancellation is possible just by means of fibral curves
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