Lectures on supergravity

TL;DR

This paper provides a comprehensive, self-contained introduction to four-dimensional N=1 supergravity, detailing its formulation, couplings, and gauge theory framework, suitable for readers with basic gauge theory and relativity knowledge.

Contribution

It offers a detailed derivation of supergravity from gauge theory principles and presents explicit off-shell formulations with matter couplings.

Findings

Clarifies supergravity as a gauge theory

Provides tensor calculus approach

Includes explicit verification of local supersymmetry

Abstract

The text is an essentially self-contained introduction to four-dimensional N=1 supergravity, including its couplings to super Yang-Mills and chiral matter multiplets, for readers with basic knowledge of standard gauge theories and general relativity. Emphasis is put on showing how supergravity fits in the general framework of gauge theories and how it can be derived from a tensor calculus for gauge theories of a standard form. Contents: 1. Introduction, 2. Gauge symmetries in the jet space approach, 3. D=4, N=1 pure supergravity, 4. Tensor calculus for standard gauge theories, 5. Off-shell formulations of D=4, N=1 supergravity with matter, A. Lorentz algebra, spinors, Grassmann parity, B. Explicit verification of local supersymmetry.