string theory

Mega-Space Current Algebra and Green-Schwarz Geometry in Heterotic String Theory

arXiv:2607.27988

summary

The paper develops a manifestly T‑dual formulation of heterotic string theory by constructing a mega‑space current algebra that unifies Lorentz and gauge connections, showing how Chern–Simons structures and the Green–Schwarz anomaly cancellation arise from algebraic identities.

Abstract

We study the Lorentz and gauge connections in heterotic string theories within a framework of manifest T-duality. A central motivation is the Bergshoeff--de Roo (BdR) type parallelism between the torsionful Lorentz and Yang-Mills connections in heterotic $I^\pm^{'}$ -corrections. We formulate worldsheet current algebras in a mega-space that incorporates the Lorentz and gauge sectors simultaneously. By generalizing the PolÃ¡Äek-Siegel scheme, we evaluate the commutators of the extended generators and determine the generalized connections. We show that this mega-space current algebra geometrically embeds the heterotic Chern--Simons structures into the generalized vielbeins and curvatures. We also show that the Green-Schwarz anomaly cancellation condition follows from the Jacobi identity for the algebra of stringy covariant derivatives, the ``nachos'' operators $▹_{M}$ .

23 pages

Topics & keywords

#heterotic string theory #t-duality #current algebra #generalized geometry #anomaly cancellationLorentz connectionYang-Mills connectionα'-correctionsmega-spaceChern–SimonsGreen–SchwarzJacobi identitygeneralized vielbein