ChernSimons (Super)Gravity

This book grew out of a set of lecture notes on gravitational Chern–Simons (CS) theories developed over the past decade for several schools and different audiences including graduate students and researchers.

CS theories are gauge-invariant theories that can include gravity consistently. They are only defined in odd dimensions and represent a very special class of theories in the Lovelock family. Lovelock gravitation theories are the natural extensions of General Relativity for dimensions greater than four that yield second-order field equations for the metric. These theories also admit local supersymmetric extensions where supersymmetry is an off-shell symmetry of the action, as in a standard gauge theory.

Apart from the arguments of mathematical elegance and beauty, the gravitational CS actions are exceptionally endowed with physical attributes that suggest the viability of a quantum interpretation. CS theories are gauge-invariant, scale-invariant and background independent; they have no dimensional coupling constants. All constants in the Lagrangian are fixed rational coefficients that cannot be adjusted without destroying gauge invariance. This exceptional status of CS systems makes them classically interesting to study, and quantum mechanically intriguing and promising.

Contents:

• The Quantum Gravity Puzzle
• Geometry: General Overview
• First Order Gravitation Theory
• Gravity in Higher Dimensions
• Chern–Simons Gravities
• Additional Features of Chern–Simons Gravity
• Black Holes, Particles and Branes
• Supersymmetry and Supergravity
• Chern–Simons Supergravities
• Inönü–Wigner Contractions and Its Extensions
• Unconventional Supersymmetries
• Concluding Remarks

Readership: This book provides an introduction to Chern–Simons (super) gravity theories accessible for physics as well as mathematics graduate students and researchers.
Key Features:

• The topics described in this book are self-contained and just require some basic background in physics and mathematics. Chern–Simons supergravity is a field which is intensively studied in the current literature of physics and mathematics, with more than 2000 articles related to this topic in the arXiv database
• This title covers a topic not usually discussed either in standard gravity courses or in mathematical presentations of characteristic classes or cohomology