2005/09/30 by Anastasios C. Petkou, George Siopsis
Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #Black Holes and Theoretical Physics #Boundary (topology) #Combinatorics #Computer science #Constant (computer programming) #Cosmological constant #Cosmology and Gravitation Theories #Coupling constant #Dimension (graph theory) #Energy (signal processing) #Gross–Neveu model #Mathematical analysis #Mathematical physics #Mathematics #Physics #Quantum mechanics #String theory #Vacuum energy #hep-th
paper · pdf · doi:10.1016/j.physletb.2006.07.062
published as Phys.Lett.B640:209-213,2006 · 10 pages, improved discussion to appear in Phys. Lett. B
arxiv created 2006/08/01 · openalex publication_date 2006/08/09 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We point out a nontrivial connection between the model proposed by Hořava and Keeler as a candidate for noncritical M-theory and the Gross–Neveu model with fermionic fields obeying periodic boundary conditions in 2+1 dimensions. Specifically, the vacuum energy of the former is identified with the large-N free-energy of the latter up to an overall constant. This identification involves an appropriate analytic continuation of the subtraction point in noncritical M-theory, which is related to the volume of the Liouville dimension. We show how the world-sheet cosmological constant may be obtained from the Gross–Neveu model. At its critical point, which is given in terms of the golden mean, the values of the vacuum energy and of the cosmological constant are 4/5 and 2/5 of the corresponding values at infinite string coupling constant.