Introduction to Gauge/Gravity Duality (1010.6134v1)

Abstract: These lectures are an introduction to gauge/gravity duality, presented at TASI 2010. The first three sections present the basics, focusing on $AdS_5 \times S^5$. The last section surveys a variety of ways to generate duals of reduced symmetry.

• The paper presents a derivation of the AdS/CFT correspondence by linking gravity in AdS space with conformal field theories on the boundary.
• It details methodologies, including hand-waving and braney derivations, to emphasize symmetry matching between bulk fields and CFT operators.
• The work extends the duality through symmetry-breaking scenarios, offering practical insights for applications in high-energy and condensed matter physics.

An Insight into Gauge/Gravity Duality

The paper "Introduction to Gauge/Gravity Duality" presented by Joseph Polchinski at TASI 2010 offers a comprehensive introduction to gauge/gravity duality, particularly focusing on its foundational aspects and extensions. This document is structured to elucidate the AdS/CFT correspondence and its implications for theoretical physics, providing updates on the evolution of our understanding of reduced symmetry duals.

Key Concepts and Derivations

Polchinski's work primarily revolves around the AdS/CFT correspondence, famously described by the equation AdS = CFT. This duality suggests that a type of string theory in anti-de Sitter (AdS) space is equivalent to a conformal field theory (CFT) on the boundary of this space. This paper explores various motivations and derivations of this duality, including:

• A Hand-Waving Derivation: This approach links gauge theory and gravity without direct reliance on string theory, postulating a connection between a massless spin-2 particle (graviton) and spin-1 gauge bosons, probing no-go theorems with the holographic principle.
• A Braney Derivation: Involves D-branes and their corresponding gauge theories, transitioning between descriptions with perturbative techniques to handle different coupling regimes.

Symmetries and States Matching

The gauge/gravity duality requires matching symmetries on both sides. AdS theories exhibit SO(D,2) conformal symmetry and those related to compact spaces like S. The CFT must then manifest these symmetries, translating to superconformal symmetries in many cases. Furthermore, particle species in AdS space align with single-trace operators in the CFT, achieving a 1-to-1 mapping necessary for rigorous duality.

Correlators and Observables

Polchinski examines the dictionary between boundary operators and bulk fields, highlighting how CFT correlators are computed using boundary limits of bulk fields. The propagator of scalar fields in AdS is utilized for these calculations, yielding expressions that verify duality through scale invariance. This paper critically discusses adjustments for different quantizations and symmetry-breaking branches, broadening the application of gauge/gravity principles.

Breaking Symmetries: Extensions and Generalizations

The later sections of Polchinski's work explore the extension of gauge/gravity duality by breaking symmetries in various ways. These include Coulomb branches, RG flows, and orbifolds, which affect the geometry and subsequently the dual field theories. Such perturbations can lead to novel dualities, suitably extending the landscape of AdS states and expanding possibilities for application, including in condensed matter physics.

Practical and Theoretical Implications

The theoretical implications of gauge/gravity duality are profound, revealing new insights into the nature of space-time, quantum gravity, and field theories. Practically, this duality allows detailed computational approaches to understand strongly coupled systems, potentially influencing fields like condensed matter physics and high-energy physics.

Future Directions

While gauge/gravity duality is robust in explaining various phenomena, future research may focus on refining the understanding of non-Fermi liquids and exploring further extensions of AdS/CFT, including cases with less symmetry or non-spherical geometries.

Conclusion

Polchinski's lectures serve as a bastion for researchers diving into the intricacies of gauge/gravity duality. By dissecting foundational equations, symmetries, and extensions, it directs readers towards both theoretical robustness and practical explorations in the field of theoretical physics. As researchers continue to develop these concepts, gauge/gravity duality may unravel more of the complex interplay between field theories and gravitational dynamics.