science

Hanany–Witten transition

Hanany–Witten transition is a science 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 Hanany–Witten transition rather than just read about it. In short: In theoretical physics the Hanany–Witten transition, also called the Hanany–Witten effect, refers to any process in a superstring theory in which two p-branes cross resulting in the creation or destruction of a third p-brane. A special case of this process was first discovered by Amihay Hanany and Edward Witten in 1996.

Key takeaways

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

Reference excerpt

In theoretical physics the Hanany–Witten transition, also called the Hanany–Witten effect, refers to any process in a superstring theory in which two p-branes cross resulting in the creation or destruction of a third p-brane. A special case of this process was first discovered by Amihay Hanany and Edward Witten in 1996. All other known cases of Hanany–Witten transitions are related to the original case via combinations of S-dualities and T-dualities. This effect can be expanded to string theory, 2 strings cross together resulting in the creation or destruction of a third string.

The original effect The original Hanany–Witten transition was discovered in type IIB superstring theory in flat, 10-dimensional Minkowski space. They considered a configuration of NS5-branes, D5-branes and D3-branes which today is called a Hanany–Witten brane cartoon. They demonstrated that a subsector of the corresponding open string theory is described by a 3-dimensional Yang–Mills gauge theory. However they found that the string theory space of solutions, called the moduli space, only agreed with the known Yang-Mills moduli space if whenever an NS5-brane and a D5-brane cross, a D3-brane stretched between them is created or destroyed. They also presented various other arguments in support of their effect, such as a derivation from the worldvolume Wess–Zumino terms. This proof uses the fact that the flux from each brane renders the action of the other brane ill-defined if one does not include the D3-brane.

The S-rule Furthermore, they discovered the S-rule, which states that in a supersymmetric configuration the number of D3-branes stretched between a D5-brane and an NS5-brane may only be equal to 0 or 1. Then the Hanany-Witten effect implies that after the D5-brane and the NS5-brane cross, if there was a single D3-brane stretched between them it will be destroyed, and if there was not one then one will be created. In other words, there cannot be more than one D3 brane that stretches between a D5 brane and an NS5 brane.

Generalizations

(p,q) 5-branes More generally, NS5-branes and D5-branes may form bound states known as (p,q) 5-branes. The above argument was extended in Branes and Supersymmetry Breaking in Three Dimensional Gauge Theories to the case of a (p,q) and a (p',q') 5-brane which cross. The authors found that the number of D3-branes created or destroyed must be equal to pq'-p'q. Furthmore they showed that this leads to a generalized S-rule, which states that in a supersymmetric configuration the number of D3-branes never goes negative upon crossing two 5-branes. If it does go negative, then the gauge theory exhibits spontaneous supersymmetry breaking.

Dual forms of the effect Via a series of T-dualities one obtains the result that in any type II superstring theory, when an NS5-brane and a Dp-brane cross one necessarily creates or destroys a D(p-2)-brane. Lifting this statement to M-theory one finds that when two M5-branes cross, one creates or destroys an M2-brane. Using S-duality one may obtain transitions without NS5-brane. For example, when a D5-brane and a D3-cross one creates or destroys a fundamental string.

References

Worked examples

Example 1 — a first encounter with Hanany–Witten transition

Start with the simplest possible case. Write down what Hanany–Witten transition claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, 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 Hanany–Witten transition 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 Hanany–Witten transition 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 Hanany–Witten transition

In research: Hanany–Witten transition appears in science 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 Hanany–Witten transition 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: Hanany–Witten transition is common in secondary-school and first-year university syllabi. It links to neighbouring topics String theory, so understanding it makes those chapters shorter.
In everyday life: Look for Hanany–Witten transition 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 Hanany–Witten transition in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Hanany–Witten transition 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 Hanany–Witten transition out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Hanany–Witten transition in simple terms?

Why does Hanany–Witten transition matter?

Because it connects several science 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 Hanany–Witten transition?

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 Hanany–Witten transition.