- The paper redefines the NSNS Lagrangian by replacing the traditional metric and B-field with a new metric and an antisymmetric bivector to encapsulate the Q-flux.
- Methodologically, it employs generalized complex geometry to achieve a field redefinition that yields a globally well-defined action in non-geometric flux compactifications.
- The analysis connects ten-dimensional reformulations to four-dimensional effective potentials via illustrative toroidal examples, highlighting implications for string theory compactifications.
A Ten-Dimensional Action for Non-Geometric Fluxes
The paper by Andriot, Larfors, Lüsta, and Patalong presents a rigorous exploration of ten-dimensional supergravity within the framework of non-geometric flux compactifications, utilizing a field redefinition inspired by Generalized Complex Geometry (GCG). The authors aim to encapsulate non-geometric Q-flux within the ten-dimensional Neveu-Schwarz-Neveu-Schwarz (NSNS) action and demonstrate its implications for four-dimensional effective field theories.
The central thesis of this work is the reformulation of the NSNS Lagrangian in terms of new field variables. Here, the transformation from the conventional metric and B-field to a new metric and an antisymmetric bivector β is pivotal. This field redefinition is anchored in GCG, where the generalized metric is invariant under O(2d) transformations, allowing for an insightful representation of non-geometric fluxes. The explicit change of variables facilitates the rewriting of the NSNS action to include a term for the Q-flux, expressed as |Q|².
A critical assumption in this derivation is that the β-field aligns with isometry directions, reducing the complexity of the computation and isolating the Q-flux contribution while excluding the R-flux. This focus on a simpler non-geometric configuration lays the groundwork for establishing the quantum characteristics of these fluxes, providing a ten-dimensional perspective on the non-geometric structures often discussed in four-dimensional supergravity theories.
An interesting result from the paper is its application to a toroidal example that illustrate the global properties of the rewritten Lagrangian. The authors find that while the original NSNS fields could become globally ill-defined in non-geometric setups, their redefined counterparts yield well-defined global actions. This assertion is significant for dimensional reduction processes, offering direct links to known four-dimensional theories with non-geometric potentials that have garnered interest for potential de Sitter solutions in string theory compactifications.
This reformulation encapsulates a significant effort to reconcile ten- and four-dimensional perspectives of non-geometry, especially in the manifestation of non-geometric Q-flux as analogous terms in four-dimensional effective potentials. Although the paper is careful not to declare its results as revolutionary, the insights gained are indeed noteworthy for providing a formal foundation for non-geometric fluxes within higher-dimensional supergravity formulations.
In summary, this work requires the engagement of an academic audience familiar with the subtleties of string theory compactifications, supergravity, and T-duality. The methodological rigor of translating GCG insights into field theoretic constructs within supergravity effectively bridges theoretical gaps between ten-dimensional string dynamics and the phenomenological exigencies of four-dimensional field theories. Further paper into the conjectured inclusion of R-flux and its potential impact on both rule-setting and phenomenological outcomes involves significant implications and remains an engaging direction for future research endeavors. The potential expansion into double field theory and its impact on string theory could offer broader insights into the fundamental architecture of non-geometric compactifications and their role in modern theoretical physics.
