The powers of monodromy

Abstract

Flux couplings to string theory axions yield super-Planckian field ranges along which the axion potential energy grows. At the same time, other aspects of the physics remain essentially unchanged along these large displacements, respecting a discrete shift symmetry with a sub-Planckian period. After a general overview of this monodromy effect and its application to large-field inflation, we present new classes of specific models of monodromy inflation, with monomial potentials µ 4−p φ p . A key simplification in these models is that the inflaton potential energy plays a leading role in moduli stabilization during inflation. The resulting inflaton-dependent shifts in the moduli fields lead to an effective flattening of the inflaton potential, i.e. a reduction of the exponent from a fiducial value p 0 to p < p 0 . We focus on examples arising in compactifications of type IIB string theory on products of tori or Riemann surfaces, where the inflaton descends from the NS-NS two-form potential B 2 , with monodromy induced by a coupling to the R-R field strength F 1 . In this setting we exhibit models with p = 2/3, 4/3, 2, and 3, corresponding to predictions for the tensor-to-scalar ratio of r ≈ 0.04, 0.09, 0.13, and 0.2, respectively. Using mirror symmetry, we also motivate a second class of examples with the role of the axions played by the real parts of complex structure moduli, with fluxes inducing monodromy.

The challenge of realizing F-term axion monodromy inflation in string theory

“…These four-dimensional axions can descend from higher p-form fields in ten dimensions, but also geometric moduli of shiftsymmetric backgrounds can show such a behavior. Recently discussed examples include the real parts of complex-structure moduli U = u + iv on a torus [7] or the deformation moduli ξ of a D7-brane wrapping a transverse four-cycle of the internal manifold [8,9]. On a generic Calabi-Yau manifold, such symmetries can also appear at special points in the moduli space, for instance in the large complex-structure limit.…”

“…In [9] the axion was identified with an open-string modulus, namely the superpartner in the Higgs sector of the MSSM. In the much-discussed example of [7] (see also [36]), the axion was considered to be the Kalb-Ramond field B integrated over an internal two-cycle, whereas in [33] it was proposed to use a D7-brane Wilson line modulus. Note that initially the latter model requires a continuous one-cycle in the internal fourcycle wrapped by the D7-brane, which becomes twisted by turning on geometric flux.…”

“…The main task therefore is to find minima of the scalar potential such that an axion, or an axion-like field, becomes the parametrically lightest scalar, whose dynamics, after integrating out all the heavier fields, is governed by a simple φ q effective potential. As proposed in [7,39], q could also be a rational number.…”

Inflation in string theory confronts data

“…3 String theory contains various scenarios for inflation. One basic mechanism, monodromy inflation [14,15,16,17,18,19,20] , realizes large-field ('chaotic') inflation generalizing the m 2 φ 2 model [10] (with elements of natural inflation [11]). This mechanism descends in a robust way from higher dimensional gauge potentials and their couplings to magnetic fluxes, as well as various analogues related by string duality symmetries.…”

“…Starting from the quadratic model, we had explained this improvement of fit in a simple way above via the energetically favorable flattening effect [12]. But as described in [20] and [19], there exist couplings in the theory which admit a starting (un-backreacted) power V ∝ φ n with higher n. In fact, n is in principle unbounded, taking into account that perturbative string theory can be formulated in any total dimensionality D, as long as one properly accounts for the tree level potential energy ∝ (D−10)g 2 ef f , with g ef f the four-dimensional effective string coupling. These models are (so far) less well studied, and involve additional fields which may have unrealistic consequences, but they raise the question of how large the theoretically-allowed region of r, n s is in this general mechanism.…”