Heterotic Quantum Cohomology

Abstract

We reexamine the massless spectrum of a heterotic string vacuum at large radius and present two results. The first result is to construct a vector bundle Q and operator D whose kernel amounts to deformations solving 'F-term' type equations. This resolves a dilemma in previous works in which the spin connection is treated as an independent degree of freedom, something that is not the case in string theory. The second result is to utilise the moduli space metric, constructed in previous work, to define an adjoint operator D † . The kernel of D † amounts to deformations solving 'D-term' type equations. Put together, we show there is a vector bundle Q with a metric, a D operator and a gauge fixing (holomorphic gauge) in which the massless spectrum are harmonic representatives of D. This is remarkable as previous work indicated the Hodge decomposition of massless deformations were complicated and in particular not harmonic except at the standard embedding.

Harmonic metrics for the Hull-Strominger system and stability

“…As in [15], we will assume throughout that the connection ∇ in the tangent bundle is Hermitian-Yang-Mills. This suggests a new point of view on the spurious degrees of freedom corresponding to the connection ∇ in the physical interpretation of the solutions, which have motivated an extensive discussion in the string theory literature (see [29] and references therein).…”

The Strominger system in the square of a Kähler class

“…Here we consider the problem of finding optimal representatives in a given balanced class. Various approaches to this question have been proposed in the literature [20,27,28,29,46,43,48,51,52], and the Strominger system [47] stands out as a natural candidate due to its importance in theoretical physics [1,5,6,9,12,39].…”