Moduli axions, stabilizing moduli, and the large field swampland conjecture in heterotic M-theory

Abstract

We compute the F- and D-term potential energy for the dilaton, complex structure, and Kähler moduli of realistic vacua of heterotic M-theory compactified on Calabi-Yau threefolds where, for simplicity, we choose h1,1=h2,1=1. However, the formalism is immediately applicable to the “universal” moduli of Calabi-Yau threefolds with h1,1=h1,2>1 as well. The F-term potential is computed using the nonperturbative complex structure, gaugino condensate and “world sheet instanton” superpotentials in theories in which the hidden sector contains an anomalous U(1) structure group. The Green-Schwarz anomaly cancellation induces inhomogeneous “axion” transformations for the imaginary components of the dilaton and Kähler modulus—which then produce a D-term potential. VD is a function of the real components of the dilaton and Kähler modulus (s and t) that is minimized and precisely vanishes along a unique line in the s−t plane. Excitations transverse to this line have a mass manom which is an explicit function of t. The F-term potential energy is then evaluated along the VD=0 line. For values of t small enough that manom≳MU—where MU is the compactification scale—we plot VF for a realistic choice of coefficients as a function of the Pfaffian parameter p. We find values of p for which VF has a global minimum at negative or zero vacuum density or a metastable minimum with positive vacuum density. In all three cases, the s, t, and associated “axion” moduli are completely stabilized. Finally, we show that, for any of these vacua, the large t behavior of the potential energy satisfies the “large scalar field” Swampland conjecture. Published by the American Physical Society 2024