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SOSpin, a C++ library for Yukawa decomposition in SO(2N) models

SOSpin (one reads it as a single word “sospin”) is a C++ Library whose purpose is to decompose Yukawa couplings invariant under SO(2N) groups in terms of the SU(N) degrees of freedom subgroup. We include specific functions to address the SO(10) case.

How to write the spinorial SO(2N) representation in terms of SU(N) states?
Answer: The Link - annihilation and creation operators - $b_i$ and $b^\dagger_i$ ! The description via wave functions is substituted by the use of creation, $\color{blue} b^{\dagger}_i$, and annihilation, $\color{blue}b^{}_i$, operators: \begin{equation*} \Psi\longrightarrow|\Psi\rangle=|0\rangle\psi \,+\,b^{\dagger}_i|0\rangle\psi^i \,+\, \frac{1}{2}\psi^{ij} \, b^{\dagger}_i b^{\dagger}_j|0\rangle \,+\, \cdots +\, \frac{1}{N!} \varepsilon^{ij\cdots k}\, \underbrace{b^{\dagger}_i b^{\dagger}_j\cdots b^{\dagger}_k}_N |0\rangle\bar{\psi} \end{equation*} Grassmann Algebra: $\{b_i,b^{\dagger}_j\}=\delta_{ij}\,\quad\text{and}\quad\{b_i,b_j\}=0=\{b^{\dagger}_i,b^{\dagger}_j\}$.

More details describing the formalism can be found in the manual.



If you use this code or parts of it, please cite the paper:

  1. Nuno Cardoso, David Emmanuel-Costa, Nuno Gonçalves, C. Simões, "SOSpin, a C++ library for Yukawa decomposition in SO(2N) models", arXiv:1509.00433, 2015.


The source is available as a tar'ed and gzip'ed package, which extracts the files into a directory called sospin-X.Y.Z. The compilation can be done by running the Install command. The code has been developed and tested under Ubuntu and Mac OSX, please report any compilation problems under other operating systems to the authors.


For those interested in SOSpin's internals, reference pages generated by Doxygen are available for the current release here.


  1. SO(4)
  2. SO(10)

SOSpin Collaboration 2015      Last modified: