Higher Spin Interactions from Conformal Field Theory: The Complete Cubic Couplings

Area of Science:

• High Energy Physics
• String Theory
• Quantum Field Theory

Background:

• Higher spin theories describe particles with spins greater than 2.
• Holographic principle relates gravity in higher dimensions to quantum field theories in lower dimensions.
• Anti-de Sitter space is a key theoretical framework in these studies.

Purpose of the Study:

• To achieve a complete holographic reconstruction of cubic couplings in minimal bosonic higher spin theory.
• To establish connections between quantum field theory models and gravitational theories.
• To analyze interactions within higher spin gauge fields.

Main Methods:

• Holographic reconstruction techniques applied to anti-de Sitter space.
• Determination of operator-product expansion (OPE) coefficients for conserved currents.
• Computation of tree-level three-point Witten diagram amplitudes.

Main Results:

• A complete holographic reconstruction of cubic couplings was achieved.
• Operator-product expansion coefficients for the d-dimensional free scalar O(N) vector model were determined.
• Tree-level three-point Witten diagram amplitudes for cubic interactions were computed.

Conclusions:

• The study provides a comprehensive understanding of cubic couplings in higher spin theories through holography.
• The results offer insights into the interplay between gauge theories and gravity.
• This work advances the holographic dictionary for higher spin theories.