Abstract
We study string loop corrections to the gravity kinetic terms in type IIB com- pactifications on Calabi-Yau threefolds or their orbifold limits, in the presence of D7-branes and orientifold planes. We show that they exhibit in general a logarithmic behaviour in the large volume limit transverse to the D7-branes, induced by a localised four-dimensional Einstein-Hilbert action that appears at a lower order in the closed string sector, found in the past. Here, we compute the coefficient of the logarithmic corrections and use them to provide an explicit realisation of a mechanism for Kähler moduli stabilisation that we have proposed recently, which does not rely on non-perturbative effects and lead to de Sit- ter vacua. Our result avoids no-go theorems of perturbative stabilisation due to runaway potentials, in a way similar to the Coleman-Weinberg mechanism, and provides a counter example to one of the swampland conjectures concerning de Sitter vacua in quantum grav- ity, once string loop effects are taken into account; it thus paves the way for embedding the Standard Model of particle physics and cosmology in string theory.
Highlights
JHEP01(2020)149 fact that the aforementioned quantum corrections have a logarithmic dependence on the moduli associated with the co-dimension two volume [10] transverse to the D7 brane
We compute the coefficient of the logarithmic corrections and use them to provide an explicit realisation of a mechanism for Kahler moduli stabilisation that we have proposed recently, which does not rely on non-perturbative effects and lead to de Sitter vacua
It is clear that these localised graviton kinetic terms can receive to the order logarithmic corrections on the size of the volume transverse to 7-brane sources localised at distant points from the graviton kinetic terms, due to the emission of closed strings on non-vanishing local tadpoles
Summary
The Dine-Seiberg problem [16] is a long-standing question in moduli stabilisation. It concerns the modulus that controls the perturbative expansion, either in α (the internal volume), or in string loops (the dilaton). The two terms could compensate each other and lead to a minimum provided that the coefficient η is negative This mechanism is reminiscent of the one with a Coleman-Weinberg potential [30], offering an alternative solution to the runaway moduli problem, consistent with perturbation theory in the large volume expansion. It follows that in order to make this solution large enough, as required in the large volume expansion, we assumed a priori that μ has to be exponentially small, which corresponds to the condition ξ −η > 0 This is again similar to the situation in the Coleman-Weinberg potential, where η and ξ correspond to two different parameters/couplings, such as a quartic scalar interaction and a gauge coupling [30]. We shall present an explicit string theory example, realising the above proposal
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