physics

Supergravity

Supergravity is a physics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Supergravity rather than just read about it. In short: In theoretical physics, supergravity (supergravity theory; SUGRA for short) is a modern field theory that combines the principles of supersymmetry and general relativity; this is in contrast to non-gravitational supersymmetric theories such as the Minimal Supersymmetric Standard Model. Supergravity is the gauge theory of local supersymmetry.

Key takeaways

Supergravity belongs to physics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Supergravity to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Supergravity from memory before moving on to harder problems.

Reference excerpt

In theoretical physics, supergravity (supergravity theory; SUGRA for short) is a modern field theory that combines the principles of supersymmetry and general relativity; this is in contrast to non-gravitational supersymmetric theories such as the Minimal Supersymmetric Standard Model. Supergravity is the gauge theory of local supersymmetry. Since the supersymmetry (SUSY) generators form together with the Poincaré algebra and superalgebra, called the super-Poincaré algebra, supersymmetry as a gauge theory makes gravity arise in a natural way.

Gravitons Like all covariant approaches to quantum gravity, supergravity contains a spin-2 field whose quantum is the graviton. Supersymmetry requires the graviton field to have a superpartner. This field has spin 3/2 and its quantum is the gravitino. The number of gravitino fields is equal to the number of supersymmetries.

History

Gauge supersymmetry The first theory of local supersymmetry was proposed by Dick Arnowitt and Pran Nath in 1975 and was called gauge supersymmetry.

Supergravity The first model of 4-dimensional supergravity (without this denotation) was formulated by Dmitri Vasilievich Volkov and Vyacheslav A. Soroka in 1973, emphasizing the importance of spontaneous supersymmetry breaking for the possibility of a realistic model. The minimal version of 4-dimensional supergravity (with unbroken local supersymmetry) was constructed in detail in 1976 by Dan Freedman, Sergio Ferrara and Peter van Nieuwenhuizen. In 2019 the three were awarded a special Breakthrough Prize in Fundamental Physics for the discovery. The key issue of whether or not the spin 3/2 field is consistently coupled was resolved in the nearly simultaneous paper, by Stanley Deser and Bruno Zumino, which independently proposed the minimal 4-dimensional model. It was quickly generalized to many different theories in various numbers of dimensions and involving additional (N) supersymmetries. Supergravity theories with N > 1 are usually referred to as extended supergravity (SUEGRA). Some supergravity theories were shown to be related to certain higher-dimensional supergravity theories via dimensional reduction (e.g. N=1, 11-dimensional supergravity is dimensionally reduced on T7 to 4-dimensional, ungauged, N = 8 supergravity). The resulting theories were sometimes referred to as Kaluza–Klein theories as Theodor Kaluza and Oskar Klein constructed in 1919 a 5-dimensional gravitational theory, that when dimensionally reduced on a circle, its 4-dimensional non-massive modes describe electromagnetism coupled to gravity.

mSUGRA mSUGRA means minimal supergravity. The construction of a realistic model of particle interactions within the N = 1 supergravity framework where supersymmetry (SUSY) breaks by a super Higgs mechanism carried out by Ali Chamseddine, Richard Arnowitt and Pran Nath in 1982. Collectively now known as minimal supergravity Grand Unification Theories (mSUGRA GUT), gravity mediates the breaking of SUSY through the existence of a hidden sector. mSUGRA naturally generates the Soft SUSY breaking terms which are a consequence of the Super Higgs effect. Radiative breaking of electroweak symmetry through renormalization group equations (RGEs) follows as an immediate consequence. Due to its predictive power, requiring only four input parameters and a sign to determine the low energy phenomenology from the scale of Grand Unification, it is widely investigated in particle physics.

11D: the maximal SUGRA One of these supergravities, the 11-dimensional theory, generated considerable excitement as the first potential candidate for the theory of everything. This excitement was built on four pillars, two of which have now been largely discredited:

Werner Nahm showed 11 dimensions as the largest number of dimensions consistent with a single graviton, and more dimensions will show particles with spins greater than 2. However, if two of these dimensions are time-like, these problems are avoided in 12 dimensions. Itzhak Bars gives this emphasis. In 1981 Ed Witten showed 11 as the smallest number of dimensions big enough to contain the gauge groups of the Standard Model, namely SU(3) for the strong interactions and SU(2) times U(1) for the electroweak interactions. Many techniques exist to embed the standard model gauge group in supergravity in any number of dimensions like the obligatory gauge symmetry in type I and heterotic string theories, and obtained in type II string theory by compactification on certain Calabi–Yau manifolds. The D-branes engineer gauge symmetries too. In 1978 Eugène Cremmer, Bernard Julia and Joël Scherk (CJS) found the classical action for an 11-dimensional supergravity theory. This remains today the only known classical 11-dimensional theory with local supersymmetry and no fields of spin higher than two. Other 11-dimensional theories known and quantum-mechanically inequivalent reduce to the CJS theory when one imposes the classical equations of motion. However, in the mid-1980s Bernard de Wit and Hermann Nicolai found an alternate theory in D=11 Supergravity with Local SU(8) Invariance. While not manifestly Lorentz-invariant, it is in many ways superior, because it dimensionally-reduces to the 4-dimensional theory without recourse to the classical equations of motion. In 1980 Peter Freund and M. A. Rubin showed that compactification from 11 dimensions preserving all the SUSY generators could occur in two ways, leaving only 4 or 7 macroscopic dimensions, the others compact. The noncompact dimensions have to form an anti-de Sitter space. There are many possible compactifications, but the Freund-Rubin compactification's invariance under all of the supersymmetry transformations preserves the action. Finally, the first two results each appeared to establish 11 dimensions, the third result appeared to specify the theory, and the last result explained why the observed universe appears to be four-dimensional. Many of the details of the theory were fleshed out by Peter van Nieuwenhuizen, Sergio Ferrara and Daniel Z. Freedman.

The end of the SUGRA era The initial excitement over 11-dimensional supergravity soon waned, as various failings were discovered, and attempts to repair the model failed as well. Problems included:

… excerpt ends here. Continue reading the full article.

Illustrations

Worked examples

Example 1 — a first encounter with Supergravity

Start with the simplest possible case. Write down what Supergravity claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In physics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Supergravity before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Supergravity ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Supergravity

In research: Supergravity appears in physics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Supergravity in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Supergravity is common in secondary-school and first-year university syllabi. It links to neighbouring topics Physics beyond the Standard Model, Supersymmetry, Theories of gravity, so understanding it makes those chapters shorter.
In everyday life: Look for Supergravity outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Supergravity in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Supergravity means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Supergravity out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Supergravity in simple terms?

Why does Supergravity matter?

Because it connects several physics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Supergravity?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Supergravity.