All-order generalized Green-Schwarz transformations

Compatibility with T-duality severely constrains higher-derivative corrections to the low-energy supergravity limits of string theory. For example, it suggests that Lorentz transformations for heterotic strings are modified in precisely the way required for the Green-Schwarz anomaly cancellation mechanism. A systematic procedure to construct the resulting generalized Green-Schwarz transformations is the generalized Bergshoeff-de Roo identification (gBdRi) ; . Although it in principle allows computing <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msup> <a:mi>α</a:mi> <a:mo>′</a:mo> </a:msup> </a:math> -corrections to higher and higher orders, technically it becomes unfeasible beyond <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:msup> <c:mrow> <c:mi>α</c:mi> </c:mrow> <c:mrow> <c:mo>′</c:mo> <c:mn>2</c:mn> </c:mrow> </c:msup> </c:math> . We revisit this problem with an alternative approach to the gBdRi, which we have recently developed. It gives rise to a very simple all-order transformation law whose closure we verify by explicitly computing the resulting gauge algebra.