Asymmetric Cosets

TL;DR

This work develops a general framework for asymmetric cosets G/H, where the left and right actions of H on G differ, leading to heterotic conformal field theories. It constructs a modular-invariant bulk partition function from embeddings ε_L, ε_R with an anomaly-cancellation constraint x_L k = x_R k, and then builds a comprehensive boundary-state program by descending from branes on G to the coset G/H, yielding a rich set of localized brane geometries. The authors apply the formalism to notable backgrounds, including the base of the conifold (T^{pq}) and the time-dependent Nappi–Witten cosmology, showcasing automorphism-type, GMM-type, and non-automorphism-type examples. The results provide a robust, exact CFT toolkit for exploring novel geometric backgrounds in string theory, with implications for both cosmological models and flux geometries.

Abstract

The aim of this work is to present a general theory of coset models G/H in which different left and right actions of H on G are gauged. Our main results include a formula for their modular invariant partition function, the construction of a large set of boundary states and a general description of the corresponding brane geometries. The paper concludes with some explicit applications to the base of the conifold and to the time-dependent Nappi-Witten background.

Figures (8)

• Figure 1: The group manifold $SU(2)$ as a fibre over the unit intervall.
• Figure 2: A second illustration of the group manifold $SU(2)$.
• Figure 3: The group manifold $SL(2,\mathbb{R})$.
• Figure 4: The group manifold $SL(2,\mathbb{R})$ after gauging.
• Figure 5: An alternative representation of the group manifold $SL(2,\mathbb{R})$ after gauging.