Gluon scattering amplitudes at strong coupling (0705.0303v4)

Abstract: We describe how to compute planar gluon scattering amplitudes at strong coupling in N=4 super Yang Mills by using the gauge/string duality. The computation boils down to finding a certain classical string configuration whose boundary conditions are determined by the gluon momenta. The results are infrared divergent. We introduce the gravity version of dimensional regularization to define finite quantities. The leading and subleading IR divergencies are characterized by two functions of the coupling that we compute at strong coupling. We compute also the full finite form for the four point amplitude and we find agreement with a recent ansatz by Bern, Dixon and Smirnov.

• The paper establishes a method using classical string configurations in AdS to compute planar gluon scattering amplitudes at strong coupling.
• It demonstrates precise agreement with known perturbative conjectures while addressing infrared divergences via dimensional regularization.
• The methodology rigorously tests the AdS/CFT duality beyond supergravity and sets the stage for analyzing more complex n-point scattering processes.

Overview of Gluon Scattering Amplitudes at Strong Coupling

The paper by Luis F. Alday and Juan Maldacena presents an exploration of gluon scattering amplitudes at strong coupling within the framework of $\mathcal{N} = 4$ super Yang-Mills (SYM) theory, utilizing the gauge/string duality (often referred to as AdS/CFT correspondence). This approach leverages the dual description of gauge theories in terms of string theory on AdS$_5 \times S^5$. The work mainly focuses on establishing a methodology for computing planar gluon scattering amplitudes by finding classical string configurations, with the gluon momenta setting boundary conditions for these strings.

Core Methodology and Results

Central to this paper is identifying classical string solutions whose actions correspond to the planar gluon scattering amplitudes at strong coupling. Such configurations are akin to the minimal surface solutions in string theory, determined by the gluon momenta at the AdS boundary. The resulting amplitudes are inherently infrared (IR) divergent, necessitating regularization to obtain finite results—a challenge addressed through the gravity version of dimensional regularization.

Key Points:

• The leading exponential behavior of the n-point scattering amplitude is conceptualized through a classical string worldsheet whose boundary conditions reflect the gluon momenta. Formally, the n-point amplitude exhibits an elegant dependence on these momenta.
• Agreement is found with the conjectured expression for the four-point amplitude posited by Bern, Dixon, and Smirnov, which suggests that the strong coupling calculation aligns well with perturbative predictions.
• The paper isolates both leading and subleading infrared divergences characterized by specific functions of the coupling constant $\lambda$. Strong coupling computations allow for the derivation of these functions, which impact the subleading IR divergent terms, broadening the understanding initiated by low-order calculations.

Implications and Theoretical Insights

The implications of these findings are manifold. First, this work provides a stringent test for the AdS/CFT duality beyond the supergravity approximation, probing deeply into the strong coupling regime. The correspondence is validated through precise agreement with known perturbative conjectures. Additionally, the methodology may serve as a foundational tool in the analysis of more complex scattering processes, extending beyond the four-point amplitudes to higher-order interactions.

From a theoretical standpoint, this research integrates seamlessly within the paradigm of exploring quantum field theories via their dual string-theoretic descriptions. It enhances the understanding of IR divergences in gauge theories, particularly in contexts demanding the extension of existing renormalization techniques into the domain of higher-dimensional theories.

Future Directions

Potential future developments suggested by this research include the extension of this framework to n-point amplitudes and further exploration into the role of integrable structures within AdS$_5 \times S^5$ sigma models. Such considerations could refine the understanding of gluon scattering beyond four-point interactions and possibly relate these processes to spin-chain dynamics in the dual string perspective.

Additionally, scrutinizing the interplay between weak and strong coupling regimes could yield a more nuanced understanding of the transition between perturbative QCD and its non-perturbative counterparts—possibly elucidating connections that are not immediately apparent within the perturbative framework.

In conclusion, the methodology and insights offered by Alday and Maldacena not only reinforce the pivotal nature of the AdS/CFT correspondence in theoretical physics but also lay the groundwork for sophisticated analyses of quantum field theories in strong coupling regimes. Such investigations continue to push the boundaries of both computational and conceptual frameworks in modern theoretical physics.