Abstract
AbstractWe introduce a dually-weighted multi-matrix model that for a suitable choice of weights reproduce two-dimensional Causal Dynamical Triangulations (CDT) coupled to the Ising model. When Ising degrees of freedom are removed, this model corresponds to the CDT-matrix model introduced by Benedetti and Henson (Phys Lett B 678:222, 2009). We present exact as well as approximate results for the Gaussian averages of characters of a Hermitian matrix A and $$A^2$$
A
2
for a given representation and establish the present limitations that prevent us to solve the model analytically. This sets the stage for the formulation of more sophisticated matter models coupled to two-dimensional CDT as dually weighted multi-matrix models providing a complementary view to the standard simplicial formulation of CDT-matter models.
Funder
NWO VENI
CNPq
FAPERJ Jovem Cientista do Nosso Estado program
Okinawa Institute of Science and Technology Graduate University
Publisher
Springer Science and Business Media LLC
Reference154 articles.
1. ’t Hooft, G., Veltman, M.J.G.: One loop divergencies in the theory of gravitation. Ann. Inst. H. Poincare Phys. Theor. A 20, 69 (1974)
2. Christensen, S.M., Duff, M.J.: Quantizing gravity with a cosmological constant. Nucl. Phys. B 170, 480 (1980)
3. Goroff, M.H., Sagnotti, A.: The ultraviolet behavior of Einstein gravity. Nucl. Phys. B 266, 709 (1986)
4. Frohlich, J.: On the triviality of lambda (phi**4) in D-dimensions theories and the approach to the critical point in D $$>$$= four-dimensions. Nucl. Phys. B 200, 281 (1982)
5. Gell-Mann, M., Low, F.E.: Quantum electrodynamics at small distances. Phys. Rev. 95, 1300 (1954)