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This is my first resource recommendation question. Kindly suggest edits so as to improvise the question if possible.

I am a junior undergraduate. I have studied Classical Mechanics (Newton's Laws, Lagrangians, Hamiltonians, Noether Theorems, Phase Space Fluid, Poisson Brackets, Liouvellie Theorem), Classical Electrodynamics (Maxwell Equations, Field Momentum, Field Energy, Maxwell Stress-Energy Tensor, Gauge Symmetries for Electric and Magnetic Fields, Retarded Potentials, Classical Theory of Radiation), Special Relativity and General Relativity (Lorentz Transformations, Relativistic Dynamics, Manifestly Relativistic Electrodynamics, Tensorial Formulation of Special Relativity, Principle of Equivalence, Riemannian Geometry, Einstein Field Equations, Schwarzschild Solutions, some other coordinate systems like Kruskal Coordinates etc., FRW Cosmology), and Quantum Mechanics (Wave Function, Operators and Observables, Hilbert Space Formalism, Wave Equation in 3D, Spin, Hydrogen Atom, and basics of Statistics, SHO with Ladder Operators, etc.). In Mathematics, my knowledge is limited to Multivariable Calculus, Complex Analysis, Special Functions, Tensor Analysis, Basics of Topology, and Basics of Group Theory. I have also read a bit of the so-called Advanced General Relativity (Cartan-Reimann Geometry, Weizenbock Spacetimes, Torsional Models, etc.).

Now, based on information I can gather in a non-mathematical way, I find SUGRA a very interesting topic and thus, I want to learn it. I am not sure how much knowledge of SUSY or QFT should be essential for SUGRA. In principle, it is a supersymmetric theory, so I guess some idea of SUSY must be essential. But from a very rough overview of books like Ortin, it seems that the symbols they have been using are only geometrical and thus, I can probably proceed with my current knowledge provided I learn some rudimentary QFT (from David Tongs or something). Kindly suggest what all should I know more to understand SUGRA. If there is some artificial way to understand some basic topics of SUGRA then also I would be interested. Like, I am reading Zweibach's String Theory book which discusses some of the String Theory without QFT and I am enjoying it. I know I will have to learn QFT eventually and I do want to and plan to. But simultaneously, my excitement for some 'fancy' stuff is irresistible.

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    $\begingroup$ Just start reading Ortin and see how far you get. The first few chapters should be accessible with your background. Simultaneously studying supersymmetric quantum mechanics will also be helpful in developing some intuition for supersymmetry. $\endgroup$
    – childofsaturn
    Commented Apr 25, 2017 at 20:29
  • $\begingroup$ If you have not already learned about the Poincaré algebra and about spinor fields, start with those two things. $\endgroup$
    – G. Smith
    Commented Apr 3, 2021 at 5:53

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Your knowledge in General Relativity will certainly come in handy. Supergravity is actually 'just' promoting supersymmetry to a gauge symmetry, so evidently you'll have to learn SUSY. Luckily, most books introduce SUSY before they start with supergravity.

Having a knowledge of QFT is certainly essential to understand supergravity. However, since supergravity includes gravity and we don't understand quantum gravity, the supergravity lagrangians are usually treated classically, so a deep understanding of QFT is not necessary (although you should still learn QFT eventually).

I would suggest the Van Proeyen & Freedman book for someone with your background if you want to understand supergravity from the superconformal calculus. In addition there is Martin's supersymmetry primer, which focuses on supersymmetry and particle phenomenology (which would require more QTF knowledge though).

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