Higher Spins & Strings (1406.6103v2)

Abstract: It is natural to believe that the free symmetric product orbifold CFT is dual to the tensionless limit of string theory on AdS3 x S3 x T4. At this point in moduli space, string theory is expected to contain a Vasiliev higher spin theory as a subsector. We confirm this picture explicitly by showing that the large level limit of the N=4 cosets of arXiv:1305.4181, that are dual to a higher spin theory on AdS3, indeed describe a closed subsector of the symmetric product orbifold. Furthermore, we reorganise the full partition function of the symmetric product orbifold in terms of representations of the higher spin algebra (or rather its $W_{\infty}$ extension). In particular, the unbroken stringy symmetries of the tensionless limit are captured by a large chiral algebra which we can describe explicitly in terms of an infinite sum of $W_{\infty}$ representations, thereby exhibiting a vast extension of the conventional higher spin symmetry.

• The paper demonstrates the dual description of string theory and higher spins by reorganizing the symmetric orbifold CFT partition function into W₍∞₎ representations.
• It employs N=4 coset models to reveal explicit multiplicities and spectral correlations that bridge higher spin theories with string theoretic predictions.
• The work outlines a framework for analyzing extended chiral algebras and symmetry enhancement, offering new insights into gauge symmetry breaking in AdS₃ contexts.

Analysis of "Higher Spins and Strings"

The paper "Higher Spins and String Theory" by Matthias R. Gaberdiel and Rajesh Gopakumar addresses the intricate relationship between a specific class of conformal field theories (CFTs) and string theory in the context of the AdS/CFT correspondence. The paper focuses on examining the duality between free symmetric product orbifold CFTs and the tensionless limit of string theory on $\text{AdS}_3 \times \text{S}^3 \times \mathbb{T}^4$. A notable aspect of this regime is the emergence of Vasiliev higher spin theory as a subset, which the authors rigorously confirm through an explicit mapping of certain CFT cosets.

Core Contributions

1. Dual Description via Coset Theories: The paper provides evidence for the duality by exploring the large level limit of $\mathcal{N}=4$ coset models. These cosets, which are dual to AdS$_3$ higher spin theories, are shown to correspond to a closed subsector of the symmetric product orbifold CFTs. This establishes a robust connection between higher spin theories and the specific regime of string theory.
2. Re-organisation of the CFT Partition Function: A key achievement in this work is the reorganisation of the symmetric product orbifold's full partition function in terms of higher spin algebra representations, specifically through its $\mathcal{W}_{\infty}$ extension. By doing so, the paper highlights the stringy's unbroken symmetries in the tensionless limit, identifying a large chiral algebra composed of an infinite sum of $\mathcal{W}_{\infty}$ representations.
3. Symmetry Enhancement and Breaking: The CFT reorganisation elucidates the extended nature of the conventional higher spin symmetry, offering a detailed look at such stringy symmetries. The findings imply a substantial enhancement of these symmetries in special limits and present a compelling method to understand the dynamic symmetries and symmetry-breaking processes intrinsic to string and higher spin theories.
4. Future Directions and Implications: This dual description and symmetry categorisation pave the way for future exploration into the breaking and restoration of gauge symmetries in string theory and the impact this has on understanding string interactions in an AdS$_3$ context. It suggests new lines of inquiry into the relationship between higher spin fields, string compactifications, and stringy vertex operator algebra.

Numerical Highlights

The paper distinctly demonstrates numerical consistency between the projected descriptions of CFT states—via $\mathcal{W}_{\infty}$ algebra representations—and existing string theoretic predictions. The authors make bold advances by identifying explicit multiplicities and detailed spectral relations accountable in both CFT and string frameworks.

Theoretical and Practical Implications

The theoretical implications are profound, offering a fresh perspective on the structure and properties of string theories in lower dimensions. Practically, this could potentially enhance computational techniques for determining stringy vertex operators within the vast landscape of string compactifications and their corresponding gauge symmetries. Furthermore, the robust embedding of higher spin theories into established string frameworks could offer new tools for understanding string dynamics in holographic dual descriptions.

Future Trajectories

This research opens several avenues for future investigations. Notably, investigating the manner in which stringy symmetries manifest in different compactification schemes or exploring the practical implementation of these extended chiral algebras in broader physics contexts are enticing directions. Additionally, leveraging this framework could elucidate properties of other superconformal CFT models and their potential string theory duals.

In conclusion, Matthias R. Gaberdiel and Rajesh Gopakumar’s work significantly advances our comprehension of the subtleties of higher spin and string theory interplay, revealing critical insights into not only theoretical constructs but also potential new methods for exploring these complex relationships.