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Designer gravity and field theory effective potentials.

Thomas Hertog1, Gary T Horowitz

  • 1Department of Physics, University of California-Santa Barbara, Santa Barbara, CA 93106, USA.

Physical Review Letters
|August 11, 2005
PubMed
Summary

We found a strong connection between supergravity solutions and field theory potentials. Gravitational solitons in anti-de Sitter space correspond to the extrema of these potentials, offering new energy conjectures.

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Area of Science:

  • Theoretical Physics
  • String Theory
  • Quantum Field Theory

Background:

  • The anti-de Sitter/conformal field theory (AdS/CFT) correspondence provides a powerful duality between gravitational theories in anti-de Sitter space and quantum field theories on its boundary.
  • Understanding the relationship between bulk supergravity solutions and boundary field theory properties is crucial for advancing this correspondence.

Purpose of the Study:

  • To investigate the precise relationship between static supergravity solutions and the extrema of field theory potentials.
  • To establish a framework for constructing gravitational solitons in anti-de Sitter space linked to field theory potential extrema.
  • To propose new positive energy conjectures based on these findings.

Main Methods:

  • Analyzing static supergravity solutions in anti-de Sitter space.
  • Identifying boundary conditions that lead to the existence of gravitational solitons.
  • Relating the masses of these solitons to the values of a given potential function V(alpha) at its extrema.
  • Interpreting the potential function V(alpha) as an effective potential for an operator in the dual conformal field theory.

Main Results:

  • Demonstrated remarkable agreement between static supergravity solutions and extrema of field theory potentials.
  • Showed that for any function V(alpha), specific boundary conditions in anti-de Sitter space ensure gravitational solitons exist precisely at the extrema of V.
  • Established that the masses of these gravitational solitons are determined by the value of V at these extrema.
  • Interpreted each V as the effective potential for a specific operator in the dual field theory.

Conclusions:

  • The study establishes a direct and quantitative link between gravitational solitons in supergravity and potential extrema in conformal field theory.
  • This connection provides a new perspective on constructing and understanding gravitational solitons and their properties.
  • The findings support the development of new positive energy conjectures within the framework of the AdS/CFT correspondence.

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