We show that two properties of heterotic string theory, originally derived using the target space heterotic supergravity, admit a natural and elegant derivation using the string worldsheet theory. The first property concerns the heterotic T-duality transformation rules, which were previously shown to admit a formulation in terms of a generalized metric involving the Yang-Mills gauge fields. We show that the same generalized metric naturally occurs in the heterotic string sigma model by requiring Yang-Mills anomaly cancellation on the world-sheet at the lowest loop order.
We then derive the heterotic Buscher rules from a duality transformation of the worldsheet theory. The second property concerns the decoupling limit of heterotic string theory that leads to heterotic matrix string theory. Recently, such a non-relativistic limit was constructed by brute force from a target space point of view, starting from the heterotic supergravity action and the heterotic T-duality rules. Instead, we show that this decoupling limit admits a simple derivation by turning on a current-current deformation in a novel sigma model describing the heterotic non-relativistic string theory, obtained from a null T-duality of the heterotic sigma model. The deformed sigma model describes the original heterotic string theory.