Geodesic Gradient Flows in Moduli Space

Geodesics in moduli spaces of string vacua are important objects in string phenomenology. In this paper, we highlight a simple condition that connects brane tensions, including particle masses, with geodesics in moduli spaces. Namely, when a brane’s scalar charge-to-tension ratio vector $-\mathrm{\nabla }\log T$ has a fixed length, then the gradient flow induced by the logarithm of the brane’s tension is a geodesic. We show that this condition is satisfied in many examples in the string landscape.