Double Field Theory Formulation of Heterotic Strings (1103.2136v2)

Abstract: We extend the recently constructed double field theory formulation of the low-energy theory of the closed bosonic string to the heterotic string. The action can be written in terms of a generalized metric that is a covariant tensor under O(D,D+n), where n denotes the number of gauge vectors, and n additional coordinates are introduced together with a covariant constraint that locally removes these new coordinates. For the abelian subsector, the action takes the same structural form as for the bosonic string, but based on the enlarged generalized metric, thereby featuring a global O(D,D+n) symmetry. After turning on non-abelian gauge couplings, this global symmetry is broken, but the action can still be written in a fully O(D,D+n) covariant fashion, in analogy to similar constructions in gauged supergravities.

• The paper introduces an extended double field theory framework that incorporates heterotic strings with non-abelian gauge couplings.
• It employs a generalized metric formalism with O(D,D+n) symmetry to ensure consistency with gauge invariance and level-matching constraints.
• The work paves the path for future advancements in string theory, particularly in exploring non-geometric compactifications and supersymmetric extensions.

Double Field Theory Formulation of Heterotic Strings: A Detailed Examination

The paper "Double Field Theory Formulation of Heterotic Strings" by Olaf Hohm and Seung Ki Kwak represents a sophisticated extension of double field theory (DFT) with applications specifically aimed at incorporating the heterotic string. In this work, the authors build on previous formulations, notably those pertaining to the bosonic string, to encompass the additional complexities of non-abelian gauge couplings present in heterotic models.

Overview of the Extended Framework

This paper generalizes the notion of DFT by extending the symmetrical framework to include heterotic strings, which introduce non-abelian gauge fields. The authors leverage a generalized metric formalism to achieve this. One significant aspect is the introduction of a global symmetry characterized by O(D,D+n), where n corresponds to the number of gauge vectors, in order to capture the full tapestry of gauge interactions. Here, additional coordinates and a corresponding covariant constraint are posited to locally eliminate these coordinates in a manner aligning with established duality principles.

Abelian and Non-Abelian Formulations

The abelian case, serving as a stepping stone to the more complex non-abelian expansion, demonstrates that the heterotic string's incorporation into DFT is conceptually straightforward, aligning neatly with familiar dimensional reductions and corresponding coset structures. The extension to non-abelian theories is characterized by the incorporation of structure constants and gauge transformations that mix traditional diffeomorphic symmetries with adjoint rotations from a Lie group perspective.

The paper intricately details the consistency conditions and constraints required to ensure gauge invariance within this novel structure. Notably, one finds that despite breaking the larger O(D,D+n) symmetry, the framework retains an invariant form akin to gauged supergravity models, showcasing a deep connection between DFT and established gravitational theories.

Mathematical and Conceptual Insights

Central to this formulation is the elegance with which the authors handle the mathematical intricacies arising from the introduction of new coordinates. The constraints and their solutions are vividly described, particularly highlighting the relations to level-matching conditions characteristic of heterotic theories. The geometry involved is not merely mathematical but reflects substantial string theoretical principles, providing a robust framework for potential future insights into non-geometric compactifications.

The approach mirrors methodologies embolden in gauged supergravity, as revealed by the careful alignment of new couplings with known theoretical structures. This connection offers fertile ground for exploring compactification schemes beyond conventional Kaluza-Klein approaches, potentially bridging the gap between geometric and non-geometric frameworks.

Implications for Future Research

Practically, this formulation paves the way for advancements in theoretical physics, specifically in the computational understanding of compactification and dualities in string theory. The symmetry structure forms a foundation from which more generalized theories might be extrapolated, accommodating even richer field interactions. The potential for discoveries within non-geometric compactification demands exploration with wider implications across quantum gravity endeavors.

Theoretically, the insights offered by Hohm and Kwak suggest avenues for extending the framework into supersymmetric domains, a task hinted at in the discussions surrounding the Siegel formalism and its connections to superspace dualities.

Conclusion

In summary, the paper succeeds in extending double field theory to accommodate the heterotic string's unique properties, offering a detailed exploration that is both mathematically rigorous and theoretically profound. Hohm and Kwak’s contributions not only enrich the existing DFT landscape but also inspire further investigations into the greater potential of string theory as it seeks to describe the universe's fundamental fabric. Importantly, their work rests on solid foundations that promise exciting future developments within the domain of string and gauge theory.