The String Landscape: On Formulas for Counting Vacua

Authors

Tamar Friedmann, University of RochesterFollow
Richard P. Stanley, Massachusetts Institute of Technology

Document Type

Article

Publication Date

4-1-2013

Publication Title

Nuclear Physics B

Abstract

We derive formulas for counting certain classes of vacua in the string/M theory landscape. We do so in the context of the moduli space of M-theory compactifications on singular manifolds with G₂ holonomy. Particularly, we count the numbers of gauge theories with different gauge groups but equal numbers of U (1) factors which are dual to each other. The vacua correspond to various symmetry breaking patterns of grand unified theories. Counting these dual vacua is equivalent to counting the number of conjugacy classes of elements of finite order inside Lie groups. We also point out certain cases where the conventional expectation is that symmetry breaking patterns by Wilson lines and Higgs fields are the same, but we show they are in fact different.

Volume

869

Issue

1

First Page

74

Last Page

88

DOI

doi.org/10.1016/j.nuclphysb.2012.11.019

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Rights

© 2012 the authors.

Comments

Archived as published.

Recommended Citation

Friedmann, Tamar and Stanley, Richard P., "The String Landscape: On Formulas for Counting Vacua" (2013). Mathematics and Statistics: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/mth_facpubs/70