# Symplectic Majorana Spinors in 5 Dimension

• A
• Francisca Ramirez
In summary, the conversation discusses the advantages of Symplectic Majorana spinors in 5 dimensions compared to Dirac spinors, particularly in supergravity where chirality is not as important. While there are no Majorana representations in 5 dimensions, symplectic Majorana spinors can be combined into a single unconstrained Dirac spinor. However, this can make it more difficult to construct five-dimensional supergravities with the most general couplings. The authors will explain how to deal with these spinors in their work.
Francisca Ramirez
I need to know if the Symplectic Majorana spinors in 5 dimension have any advantage with respect to the Dirac spinors in 5 dimension, since they have the same number of components. For example if the Symplectic Majorana spinors have a manifested symmetry that the Dirac spinors don't have, or if it's more easy to work with the Symplectic Majorana spinors.

No, i have not see it. I am going to check it.
Thank you!

Well, just a small hint: they got their name from a certain symm. property :P

Especially in supergravity, where chirality often is not that important, we like Majorana spinors. In 2,3 and 4 dimensions we can define them, but in 5 dimensions we can't. But we can go the the next best thing: symplectic Majorana. Van Proeyen explains how and why.

Tomas Ortin, in appendix D of "Gravity and Strings" (SECOND edition), says
There are no Majorana representations in d = 5, but only pairs of (complex) symplectic-Majorana spinors that can be combined into a single unconstrained Dirac spinor. Doing this, however, hides this structure and makes it more difficult (or impossible) to construct five-dimensional supergravities with the most general couplings. We will show how to deal with these spinors...
but in Australia, Google's preview is limited and doesn't let me see the actual argument.

Thank you very mach!

## 1. What are symplectic Majorana spinors in 5 dimensions?

Symplectic Majorana spinors in 5 dimensions are mathematical objects that describe the spin degrees of freedom of particles in a 5-dimensional space. They are a combination of symplectic spinors and Majorana spinors, which are both types of mathematical spinors that have important applications in physics and mathematics.

## 2. What is the significance of studying symplectic Majorana spinors in 5 dimensions?

Studying symplectic Majorana spinors in 5 dimensions allows us to better understand the dynamics of particles in higher-dimensional spaces. This is important in theoretical physics, as many theories propose the existence of extra dimensions beyond the three spatial dimensions we are familiar with. Additionally, symplectic Majorana spinors have been used in various mathematical fields, such as differential geometry and representation theory.

## 3. How are symplectic Majorana spinors in 5 dimensions used in physics?

Symplectic Majorana spinors in 5 dimensions are used in various areas of physics, such as string theory, supersymmetry, and quantum field theory. They are particularly useful in the study of higher-dimensional theories and have been applied in the search for a unified theory of quantum mechanics and gravity.

## 4. Are symplectic Majorana spinors in 5 dimensions experimentally verified?

There is currently no direct experimental evidence for symplectic Majorana spinors in 5 dimensions. However, their predictions have been tested indirectly through experiments in particle physics, and their mathematical properties have been thoroughly studied and verified through various techniques.

## 5. Can symplectic Majorana spinors in 5 dimensions have practical applications?

While symplectic Majorana spinors in 5 dimensions have important applications in theoretical physics and mathematics, they do not have any direct practical applications in everyday life. However, the theories and concepts related to symplectic Majorana spinors have led to advancements in fields such as quantum computing and high-energy physics research.

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