- The paper advances a holographic dictionary that correlates bulk fields with boundary operators in Lifshitz-invariant models.
- It employs gravitational models, including massive vector fields and higher derivative gravity, to capture non-relativistic dynamics.
- The study reveals unique features in correlation functions and hydrodynamics, highlighting stability and transport in strongly coupled systems.
Overview of Lifshitz Holography
Lifshitz holography offers a framework for studying non-relativistic field theories via gravitational models, specifically addressing systems with Lifshitz symmetry. This paper reviews significant progress in developing a holographic dictionary for Lifshitz backgrounds, focusing on the correspondence between bulk fields and boundary operators and the features of operator correlation functions. The main goal is to deduce universal characteristics of strongly coupled Lifshitz theories described by gravitational models.
Background and Motivation
The gauge/gravity duality provides a powerful tool to explore strongly coupled relativistic field theories via gravity in higher spatial dimensions. A prominent example is the AdS/CFT correspondence, traditionally applied to quark/gluon plasma physics and various condensed matter systems. Lifshitz holography extends these concepts to non-relativistic physics, which is crucial for understanding phenomena like fermions at unitarity and high-temperature superconductors, where traditional relativistic approaches prove inadequate.
Lifshitz Symmetry and Non-relativistic Theories
Non-relativistic systems exhibit distinct symmetry properties compared to relativistic ones. Lifshitz invariant theories, characterized by an anisotropic scaling symmetry with a dynamical exponent z, lack some conventional relativistic features such as special conformal transformations. This paper elaborates on how these symmetries manifest in higher-dimensional geometries and provides mechanisms to establish gravity duals for such non-relativistic Lifshitz theories.
Gravity Duals and Holographic Modelling
The construction of gravity models realizing Lifshitz symmetry displays diverse approaches, ranging from bottom-up models using massive vectors to configurations in higher derivative gravity. The paper investigates conditions under which these geometries are physically viable, discussing the stability of backgrounds and correlating dual matter fields. Critical discussions include these models' realization, stability, related black hole solutions, and compatibility with physically reasonable matter.
Holographic Dictionary
A significant focus is the establishment of a holographic dictionary that translates bulk field behavior into boundary operator characteristics. The generalization of the AdS/CFT dictionary to Lifshitz scenarios has proven intricate, with recent advancements offering detailed insights. Despite progress, the dictionary for Lifshitz theories remains not fully concrete, posing challenges in identifying boundary operator dimensions and their correlations.
Correlation Functions and Hydrodynamics
The paper observes that correlation functions in Lifshitz theories are not completely defined by symmetry alone, leading to unique and powerful predictions from holography that can characterize these systems. Moreover, the paper evaluates hydrodynamic aspects from holographic perspectives, highlighting transport coefficients, thermodynamics, and constraints imposed by symmetry.
Newton-Cartan Geometry and Other Developments
In certain holographic models, Newton-Cartan geometry emerges as pertinent, providing enhanced symmetries that could play roles in field theories dual to Lifshitz spacetimes. The paper also notes theoretical excursions into dynamical geometries and their potential implications for understanding holographic correspondences.
Conclusion and Open Questions
The paper closes by emphasizing unresolved challenges, such as technical complexities in computations for Lifshitz models compared to relativistic scenarios, and questions regarding enhanced symmetry structures in holographic theories. Continuous investigation into Lifshitz holography could refine our understanding of non-relativistic quantum systems, contributing to broad applications in condensed matter physics and beyond.
Through this meticulous review, the author presents Lifshitz holography's theoretical underpinnings, making significant strides in aligning non-relativistic physics with gravity-based descriptions, yet acknowledging that several aspects require further scholarly attention.