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

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.