Backreaction issues in axion monodromy and Minkowski 4-forms

Abstract

Abstract:We clarify the differences between the usual Kaloper-Sorbo description of axion monodromy and the effective axionic potential in terms of Minkowski 4-forms derived in string compactifications. The fact that the metric of the 3-form fields coming from string theory is field dependent (unlike in Kaloper-Sorbo) leads to the backreaction issues recently studied in axion monodromy models within string theory. We reanalyse these problems in terms of the 4-forms focusing on the case in which the non-periodic scalars backreact on the Kahler metric of the inflaton reducing the physical field range. In the closed string sector of Type II Calabi-Yau compactifications with fluxes the metric becomes field dependent precisely when ∆φ ∼ M p , independently of the choice of fluxes. We propose, however, some counter-examples to this universal behaviour by including open string fields.

Three-forms in supergravity and flux compactifications

“…A possible role of three-forms in the solution of the strong CP problem was discussed e.g. in [16][17][18][19][20][21] and in inflationary models in [22][23][24][25][26][27]. In the context of four-dimensional global and local supersymmetric theories, three-form gauge fields can be naturally incorporated as auxiliary fields of supermultiplets, as e.g.…”

Backreaction in Axion Monodromy, 4-forms and the Swampland

“…This occurs whenever the inflaton mass can be set to zero without destabilising the rest of the scalars, so the true minimum is a deformation of the old minimum (the one obtained before stabilizing the inflaton). A good inflaton candidate to realise this feature is a D7-brane position modulus in Type IIB orientifold compactifications [19,20]. However, the mass hierarchy required to delay backreaction is not achievable in a toroidal compactification of Type IIB (or in F-theory on K3 × K3) [21].…”

“…More details of the derivation can be found in [19,30]. From here one can read the metrics Z ab (s) in (2.6) which indeed depend on the saxions via volume factors labelled by k and the field metrics g i j and c IJ in the Kähler and complex structure moduli space respectively.…”

“…Then we will show that the flux-independence of the critical field value at which the logarithmic scaling appears is a specific feature of these models and not a universal behaviour of string theory. The criterium is simple: everytime the inflaton potential can be set to zero without destabilising the rest of the scalars, the model enjoys the requirements to be able to delay the backreaction effects by generating a mass hierarchy between the inflaton and the other scalars [19,20]. However, a closer analysis reveals that, at least in flux toroidal compactifications, this mass hierarchy cannot be achieved without getting into trouble with the Kaluza-Klein scale and leaving the regime of validity of the effective theory [21], supporting this way the Refined Swampland Conjecure.…”

“…This proceedings article is based on [19] and the talk given at the "Workshop on Geometry and Physics" at Ringberg Castle in Germany. It is organised as follows.…”