Pure Connection Formalism for Gravity: Linearized Theory

Understand

We give a description of gravitons in terms of an SL(2,C) connection field.

• The gauge-theoretic Lagrangian for gravitons is simpler than the metric one.
• Moreover, all components of the connection field have the same sign in front of their kinetic term, unlike what happens in the metric formalism.
• The gauge-theoretic description is also more economic than the standard one because the Lagrangian only depends on 8 components of the field per spacetime point as compared to 10 in the Einstein-Hilbert case.