Effective 3D theory at large Nt

This is an application in C++ written as part of my PhD work to carry out the combinatorics of the effective 3D theory for lattice QCD first proposed in 1111.4953. This is the software that was used to compute the 8th order diagrams first published in 1512.05195. Eight is in no way a limit for the application, which can in principle do any order.

Prerequisites

The compiler requires C++11 support. Boost is also required and assumed to be in the default include-path.

Use

Simply run make to build the application, the executable is by default placed in obj/debug/main.out. One can change the build mode by setting the BUILD_MODE environment flag. At the moment the only value other than debug which has any specific behavour is release which turns off debug flags and sets -O3 compiler optimisation.

Running the program is trivial and is simply

obj/${BUILD_MODE}/main.out N

where N is the order one wishes to compute. The program creates 3 files in a folder named Configuration which are named kappaN.terms, kappaN.debug and kappaN.json. The files contain the following

.terms

A simple list of all the terms contributing to the effective action in W(n,m) notation as defined in 1512.05195, followed by a prefactor and the power of the number of degenerate quark flavours.

.debug

Similar to .terms however it is also shown which p and m configuration it originated from, which contraction has been done as well as which spatial index assignment. The appendix of 1512.05195 should be confronted for more detail.

.json

Again the same information as in .terms but this time in a computer readable .json format. Json parsers and printers along with the apropriate storage classes might be published on a separate occation. In this case a link will be posted here. The json format is the following

{
  "terms":
  [
    {
      "pref": "1\/12",
      "N_tr": "1",
      "factors":
      [
        {
          "n": "1",
          "m": "1",
          "pos": "{0,0,0,0}"
        },
        {}
      ]
    },
    {}
  ]
}

Notes

The software was developed during my PhD studies under the supervision of Prof. Owe Philipsen at Goethe University Frankfurt.

The makefile system in use is nonrec-make by aostruszka.

TODO

• Implement a more configurable user interface with better error messages
• Write documentation for the main program, not only the helper function library
• If time permits it should be possible to extend the code to compute the full effective theory also for small N_t