Integrability and Conformal Bootstrap: One Dimensional Defect CFT (2107.08510v2)

Abstract: In this letter we study how the exact non-perturbative integrability methods in 4D N=4 Super-Yang-Mills can work efficiently together with the numerical conformal bootstrap techniques to go beyond the spectral observables and access previously unreachable quantities such as correlation functions at finite coupling. In the setup of 1D defect CFT living on a Maldacena-Wilson line, we managed to compute with good precision a non-supersymmetric structure constant for a wide range of the `t Hooft coupling. Our result is particularly precise at strong coupling and matches well with the recent analytic results of Meneghelli and Ferrero.

• The paper presents a hybrid approach that fuses QSC integrability with numerical conformal bootstrap to compute a non-supersymmetric structure constant.
• It achieves high-precision results over a wide range of ’t Hooft couplings, effectively linking weak and strong coupling regimes.
• The study demonstrates the potential to extend these methods to other defect theories, deepening our understanding of 𝒩=4 SYM.

Integrability and Conformal Bootstrap in One-Dimensional Defect CFTs

The paper discusses the integration of exact non-perturbative integrability methods with numerical conformal bootstrap techniques to explore correlation functions in four-dimensional $\mathcal{N}=4$ Super Yang-Mills (SYM) theory. The focus particularly lies on one-dimensional defect conformal field theory (CFT) realized on a Maldacena-Wilson line. This research achieves remarkable precision in calculating a non-supersymmetric structure constant over a wide range of 't Hooft couplings, aligning closely with recent analytical findings.

Key Contributions

The paper introduces a significant advancement in the ability to compute non-supersymmetric structure constants using a hybrid approach that combines the Quantum Spectral Curve (QSC) methodology, traditionally applied to spectral observables, with Numerical Conformal Bootstrap (NCB) techniques. This methodology allows the exploration of previously inaccessible aspects of SYM, such as finite-coupling correlation functions.

One-Dimensional Defect CFT

The research targets a defect CFT represented by operators living on the infinite straight 1/2-BPS Maldacena-Wilson line in $\mathcal{N}=4$ SYM. The system preserves a subset of the full superconformal symmetry, which plays a crucial role in analyzing the correlation functions of various operators inserted along the Wilson line.

Numerical and Theoretical Methodology

By leveraging the integrability features in $\mathcal{N}=4$ SYM, the authors employ the QSC approach to obtain high-precision numerical values of dimensions and structure constants of operators in the defect CFT. The hybrid method efficiently calculates nontrivial structure constants across varying coupling regimes by integrating results from both QSC methods and numerical conformal bootstrap constraints.

Results

The paper presents a precise calculation of a key structure constant for a range of 't Hooft couplings, effectively interpolating between existing weak- and strong-coupling analytical results. The accuracy of these numerical results is emphasized at strong couplings, closely matching predictions made by Meneghelli and Ferrero using different techniques. The computational approach utilized demonstrates robustness by correctly capturing the quantum spectrum associated with the defect CFT.

Implications

The implications of integrating QSC and NCB methodologies extend beyond facilitating the calculation of previously inaccessible correlation functions. The demonstrated efficacy of these methods suggests potential extensions to broader contexts within CFTs, such as application to other dimensional anomalies and defect theories beyond $\mathcal{N}=4$ SYM. The work represents a critical step toward the analytical solution of superconformal theories by combining numerical precision with the robust theoretical frameworks provided by integrability and bootstrap methods.

Future Directions

The presented framework raises several opportunities for future research, particularly in exploring higher-dimensional analogous setups or further refining the precision of such calculations. Additionally, other CFTs exhibiting some form of partial integrability could benefit from these combined methodologies, potentially accelerating our understanding of non-perturbative phenomena in quantum field theories.

In conclusion, the paper illuminates the power of combining integrable structures with bootstrap techniques, marking substantial progress in the paper of one-dimensional defect CFTs within SYM, and paving the way for deeper insights into the dynamics of strongly-coupled gauge theories.