TY - JOUR

T1 - Matter field Kähler metric in heterotic string theory from localisation

AU - Blesneag, Ştefan

AU - Buchbinder, Evgeny I.

AU - Constantin, Andrei

AU - Lukas, Andre

AU - Palti, Eran

PY - 2018/4/1

Y1 - 2018/4/1

N2 - We propose an analytic method to calculate the matter field Kähler metric in heterotic compactifications on smooth Calabi-Yau three-folds with Abelian internal gauge fields. The matter field Kähler metric determines the normalisations of the N = 1 chiral superfields, which enter the computation of the physical Yukawa couplings. We first derive the general formula for this Kähler metric by a dimensional reduction of the relevant supergravity theory and find that its T-moduli dependence can be determined in general. It turns out that, due to large internal gauge flux, the remaining integrals localise around certain points on the compactification manifold and can, hence, be calculated approximately without precise knowledge of the Ricci-flat Calabi-Yau metric. In a final step, we show how this local result can be expressed in terms of the global moduli of the Calabi-Yau manifold. The method is illustrated for the family of Calabi-Yau hypersurfaces embedded in ℙ 1× ℙ 3 and we obtain an explicit result for the matter field Kähler metric in this case.

AB - We propose an analytic method to calculate the matter field Kähler metric in heterotic compactifications on smooth Calabi-Yau three-folds with Abelian internal gauge fields. The matter field Kähler metric determines the normalisations of the N = 1 chiral superfields, which enter the computation of the physical Yukawa couplings. We first derive the general formula for this Kähler metric by a dimensional reduction of the relevant supergravity theory and find that its T-moduli dependence can be determined in general. It turns out that, due to large internal gauge flux, the remaining integrals localise around certain points on the compactification manifold and can, hence, be calculated approximately without precise knowledge of the Ricci-flat Calabi-Yau metric. In a final step, we show how this local result can be expressed in terms of the global moduli of the Calabi-Yau manifold. The method is illustrated for the family of Calabi-Yau hypersurfaces embedded in ℙ 1× ℙ 3 and we obtain an explicit result for the matter field Kähler metric in this case.

KW - Flux compactifications

KW - Superstrings and Heterotic Strings

UR - http://www.scopus.com/inward/record.url?scp=85046496390&partnerID=8YFLogxK

U2 - 10.1007/JHEP04(2018)139

DO - 10.1007/JHEP04(2018)139

M3 - Article

AN - SCOPUS:85046496390

SN - 1126-6708

VL - 2018

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

IS - 4

M1 - 139

ER -