Abstract
We study possible string theory compactifications which, in the low-energy limit, describe chaotic inflation with a stabilizer field. We first analyze type IIA setups where the inflationary potential arises from a D6-brane wrapping an internal three-cycle, and where the stabilizer field is either an open-string or bulk K\"ahler modulus. We find that after integrating out the relevant closed-string moduli consistently, tachyonic directions arise during inflation which cannot be lifted. This is ultimately due to the shift symmetries of the type IIA K\"ahler potential at large compactification volume. This motivates us to search for stabilizer candidates in the complex structure sector of type IIB orientifolds, since these fields couple to D7-brane Wilson lines and their shift symmetries are generically broken away from the large complex structure limit. However, we find that in these setups the challenge is to obtain the necessary hierarchy between the inflationary and Kaluza-Klein scales.
Highlights
In cases where the inflaton candidate is a complex structure modulus in type IIB flux compactifications, such techniques were applied in [17,18,19]
We study possible string theory compactifications which, in the low-energy limit, describe chaotic inflation with a stabilizer field
No shift symmetry should be present for S or this field develops a tachyonic direction when taking into account the backreaction of heavy moduli during inflation
Summary
Describing inflation with low-energy effective string actions can often be split into two problems. In cases where all ρi appear logarithmically in the Kahler potential, the effective potential for the fields φi at leading order reduces to the scalar potential of the inflationary sector alone, as if the moduli had not been present as dynamical degrees of freedom This is true as long as all moduli masses, determined by the second derivatives of Wmod(ρi), lie above the Hubble scale H, determined by Winf and its first derivatives. Since DρiWmod = 0 this confirms a naive expectation fuelled by old QFT arguments: if they are heavy enough and do not break supersymmetry, the moduli completely decouple This statement is true up to sub-leading corrections which arise in powers of H/mρi, cf [29] for details. Corrections due to the finiteness of mρi — such as the flattening corrections mentioned above — cannot be obtained in this way
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