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Gravity dual to a quantum critical point with spontaneous symmetry breaking
Steven S Gubser1, Fábio D Rocha
1Joseph Henry Laboratories, Princeton University, Princeton, New Jersey 08544, USA.
Physical Review Letters
|March 5, 2009
Summary
This study explores the Abelian Higgs model with gravity, revealing unique geometries with two anti-de Sitter spaces. Unusual infrared scaling of transport coefficients, like conductivity, was observed.
Area of Science:
- Theoretical Physics
- High Energy Physics
- Condensed Matter Physics
Background:
- The Abelian Higgs model is fundamental in particle physics.
- Understanding quantum field theories coupled to gravity is crucial.
- Negative cosmological constants are relevant for models of the universe.
Purpose of the Study:
- To investigate zero-temperature solutions of the Abelian Higgs model coupled to gravity.
- To analyze the geometric properties and emergent phenomena in such systems.
- To explore the behavior of transport coefficients in the infrared regime.
Main Methods:
- Solving the Abelian Higgs model equations in the presence of gravity and a negative cosmological constant.
- Analyzing the resulting spacetime geometry, specifically identifying anti-de Sitter spaces.
- Calculating Green's functions and transport coefficients to study their scaling behavior.
Main Results:
- The model yields a geometry with two copies of anti-de Sitter space.
- Distinct conformal invariance is present in the ultraviolet and infrared.
- Effective signal propagation speed decreases in the infrared.
- Transport coefficients exhibit unusual power-law scaling in the infrared.
Conclusions:
- The studied system exhibits rich emergent behavior due to the interplay of the Abelian Higgs model, gravity, and a negative cosmological constant.
- The infrared properties, including conductivity scaling, differ significantly from standard expectations.
- These findings offer insights into quantum field theories in curved spacetimes and potential applications in condensed matter systems.
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