2024/12/19 by de la Ossa, Xenia, Larfors, Magdalena, Magill, Matthew +1
#FOS: Physical sciences #High Energy Physics - Theory (hep-th)
paper · doi:10.48550/arxiv.2412.14715
Compactifications of the heterotic string, to first order in the α' expansion, on manifolds with integrable G2 structure give rise to three-dimensional \cal N = 1 supergravity theories that admit Minkowski and AdS ground states. As shown in arXiv:1904.01027, such vacua correspond to critical loci of a real superpotential W. We perform a perturbative study around a supersymmetric vacuum of the theory, which confirms that the first order variation of the superpotential, δW, reproduces the BPS conditions for the system, and furthermore shows that δ2 W=0 gives the equations for infinitesimal moduli. This allows us to identify a nilpotent differential, and a symplectic pairing, which we use to construct a bicomplex, or a double complex, for the heterotic G2 system. Using this complex, we determine infinitesimal moduli and their obstructions in terms of related cohomology groups. Finally, by interpreting δ2 W as an action, we compute the one-loop partition function of the heterotic G2 system and show it can be decomposed into a product of one-loop partition functions of Abelian and non-Abelian instanton gauge theories.