Closer towards inflation in string theory

TL;DR

The paper investigates slow-roll brane inflation within string compactifications by enforcing a shift symmetry that protects the inflaton mass. It derives how this symmetry constrains the superpotential to a form $W( ho,oldsymbol{ phi})=F( ho- frac{1}{2}oldsymbol{ phi}^2)\,e^{ieta_ioldphi_i}$, or equivalently $W(oldsymbol{oldsymbol{ sigma}},oldphi)=F(oldsymbol{ sigma})e^{ieta_ioldphi_i}$ with $oldsymbol{ sigma}= ho- frac{1}{2}oldsymbol{ phi}^2$, yielding remnant flat directions suitable for slow-roll. In KKLT-type constructions with D3-$ar{D}$3 inflation, the shift symmetry can be preserved in the uplifting term $V_{ar{D}3}$, while non-perturbative effects from D7-branes generate $W$ that depend on the shifted modulus, sustaining inflation along flat directions. The analysis extends to D3-D7 systems, where a relative brane position remains the inflaton and a remnant shift symmetry imposes a degenerate SUSY vacuum with flat directions, offering a symmetry-based criterion for slow-roll viability beyond detailed microphysical specifications. Overall, the work highlights how a shift-symmetry perspective can determine the possibility of slow-roll inflation in string theory and emphasizes the role of SUSY vacuum structure and a landscape of metastable vacua in cosmological realizations.

Abstract

In brane inflation, the relative brane position in the bulk of a brane world is the inflaton. For branes moving in a compact manifold, the approximate translational (or shift) symmetry is necessary to suppress the inflaton mass, which then allows a slow-roll phase for enough inflation. Following recent works, we discuss how inflation may be achieved in superstring theory. Imposing the shift symmetry, we obtain the condition on the superpotential needed for inflation and suggest how this condition may be naturally satisfied.