Unification of Type II Strings and T-duality (1106.5452v2)

Abstract: We present a unified description of the low-energy limits of type II string theories. This is achieved by a formulation that doubles the space-time coordinates in order to realize the T-duality group O(10,10) geometrically. The Ramond-Ramond fields are described by a spinor of O(10,10), which couples to the gravitational fields via the Spin(10,10) representative of the so-called generalized metric. This theory, which is supplemented by a T-duality covariant self-duality constraint, unifies the type II theories in that each of them is obtained for a particular subspace of the doubled space.

A Unified Description of Type II Strings and T-Duality

The paper "Unification of Type II Strings and T-duality" by Hohm, Kwak, and Zwiebach provides a comprehensive framework to unify the low-energy limits of type IIA and type IIB string theories through a geometric realization of T-duality. Utilizing an innovative formulation that incorporates doubled space-time coordinates, the authors aim to encapsulate the O(10,10) T-duality group into the fabric of string theory, thereby introducing an advanced approach to recasting conventional fields and interactions.

In string theory, T-duality is a symmetry that relates type IIA and type IIB string theories; it plays a vital role in demonstrating that ostensibly distinct theories can be considered different facets of a single structure. The authors focus on Double Field Theory (DFT), which historically enabled a symmetry group O(D,D) prior to dimensional reduction. In the presented framework, the authors extend DFT by incorporating the Ramond-Ramond (RR) fields as spinors of O(10,10). This extension aims to treat type IIA and type IIB theories uniformly within the scope of a generalized metric and spinorial formulation.

A notable aspect of the paper is the treatment of NS-NS and RR sectors using a democratic formulation that brings forth the elegance of T-duality in unifying string theories. The generalized metric $H$ and spinor $\chi$ represent NS-NS and RR fields, respectively. The authors adeptly navigate the complexities associated with the formulation of spin representatives and gamma matrices, ensuring consistency across transformations like time-like T-dualities that challenge traditional interpretations of field dynamics.

From a numerical standpoint, the paper establishes the invariance of an action under gauge transformations and details the duality invariant constraints that govern the system. Key equations, such as the generalized Ricci tensor $R_{MN}$ and the energy-momentum tensor $E_{MN}$, play critical roles in expressing the dynamics and symmetries of the resulting action. Notably, the action conforms to the anticipated duality relations between RR fields, paving the way for unified descriptions across different T-duality frames.

The implications of this research are significant both theoretically and practically. The formulation holds potential to bridge gaps in understanding the underpinnings of string theory and could possibly serve as a foundation for constructing low-energy limits of an elusive full-fledged type II string field theory. The symmetry enhancements introduced by the doubling of coordinates and the subsequent resolution of RR fields within this framework could provide insights into higher-dimensional supergravities and quantum gravitational theories.

Future work may extend this framework to explore new geometrical structures inherent in string theory or examine the applicability of these structures in alternative compactifications and non-trivial topologies. The unification approach initiated by this paper could be pivotal for developing advanced models of quantum gravity that address generative space-time symmetries at every level.

In conclusion, this paper situates itself as an important contribution towards the ultimate goal of a unified theory in the string theoretical landscape, extending our understanding of T-duality and its profound implications in the unification of type II strings. It offers a refined perspective on the formulation of DFT and advances a methodological approach to integrating diverse aspects of string theories through coherent and symmetrical principles.