Correlation functions for non-conformal D$p$-brane holography (2503.18770v2)

Abstract: We use holography to study correlation functions of local operators in maximally supersymmetric Yang-Mills theories arising on the world-volume of D$p$-branes in the large-$N$ and strong-coupling limit. The relevant supergravity backgrounds obtained from the near-horizon limit of the D$p$-branes enjoy a scaling similarity, which leads to an auxiliary AdS space of fractional dimension. This suggests that holographic correlation functions in this setup can be computed by integrating standard CFT correlators over the auxiliary extra dimensions. We apply this prescription to analytically compute two- and three-point correlators of scalar operators. The resulting two-point functions take a familiar CFT form but with shifted conformal dimensions, while the three-point correlators have a much more involved position dependence which we calculate explicitly in terms of a sum of Appell functions.

Correlation Functions for Non-Conformal D$p$-Brane Holography

The paper of correlation functions through the lens of holography offers deep insights into the dynamics of strongly coupled quantum field theories (QFTs). In the paper under discussion, the authors explore the holographic calculation of correlation functions in non-conformal settings specifically associated with D$p$-brane configurations in string theory. This work is aimed at extending the celebrated AdS/CFT correspondence beyond conformal theories to include non-conformal counterparts, thereby widening the applicability of holographic methods in theoretical physics.

At the heart of the analysis is the consideration of supergravity backgrounds arising from the near-horizon limit of D$p$-branes. These configurations are characterized by their departure from conformal symmetry while still maintaining a form of scaling similarity. The paper builds on the idea that in such settings, holography can be effectively implemented by leveraging an auxiliary AdS space of fractional dimension. This auxiliary space allows the authors to derive correlation functions that are otherwise challenging to compute directly in the non-conformal theories.

Key Contributions

1. Analytical Computation of Correlators: The authors focus on the computation of two- and three-point correlation functions of scalar operators. The two-point functions are shown to take a form akin to conformal field theory (CFT) correlators but with shifted scaling dimensions due to the non-conformal nature of the underlying theory. This shift is intricately related to the scaling similarity of the D$p$-brane backgrounds.
2. Appell Function Representation: The three-point functions exhibit a complex position dependence that the authors manage to express explicitly in terms of a sum of Appell functions. This intricate mathematical formulation underscores the non-trivial structure of interactions in the non-conformal regime and provides a novel tool for analyzing such systems.
3. Scaling Similarity and Auxiliary AdS: A pivotal concept in the paper is the exploitation of a scaling similarity inherent in the supergravity solutions. This feature suggests the existence of an auxiliary higher-dimensional AdS structure, which facilitates the computational treatment of holographic correlators by integrating over extra-dimensional spaces.

Implications and Future Directions

The results presented in the paper have significant implications both theoretically and practically:

• Holographic Techniques:

The methodology applied provides a promising framework for examining other non-conformal systems where traditional CFT methods are inapplicable. The use of auxiliary dimensions to manipulate correlation functions may find broader applications in complex holographic setups.

• Non-Conformal QFT Analysis:

By elucidating the structure of non-conformal correlators, the paper paves the way for future research in understanding the dynamics of non-conformal QFTs. This could involve exploring new physical systems that are effectively described by similar non-conformal frameworks.

• Potential Tests and Extensions:

The authors propose various directions for future work, such as performing precise supergravity calculations to verify the analytical results derived, exploring additional KK-mode interactions, and investigating the role of supersymmetric Ward identities in constraining correlation structures.

In conclusion, this research offers a significant advance in our understanding of non-conformal holography, demonstrating effective strategies for computing correlation functions in theories that challenge the scope of traditional conformal techniques. The analytical tools developed herein, particularly those involving Appell functions and auxiliary dimensions, open up new avenues for the exploration of strongly interacting fields in non-conformal settings.