Fermions and emergent noncommutative gravity

Abstract

Fermions coupled to Yang-Mills matrix models are studied from the point of view of emergent gravity. We show that the simple matrix model action provides an appropriate coupling for fermions to gravity, albeit with a non-standard spin connection. Integrating out the fermions in a nontrivial geometrical background induces indeed the Einstein-Hilbert action and a dilaton-like term, at least for on-shell geometries. This explains and precisely reproduces the UV/IR mixing for fermions in noncommutative gauge theory, extending recent results for scalar fields. It also explains why some UV/IR mixing remains even in supersymmetric models, except in the N = 4 case.

On the quantum structure of space-time, gravity, and higher spin in matrix models

“…Even though it is not manifest in the action, loop corrections may lead to significant Lorentz-violating effects. For example, the induced gravity action will contain unwanted terms such as R µναβ θ µν θ αβ , where R µναβ is the Riemann tensor of the effective metric [35], which is dynamical [36,37]. This issue is resolved on covariant quantum spaces, where the fixed θ µν is replaced by a bundle-like variety of different {θ µν } over space-time, which is effectively averaged.…”

Emergent noncommutative gravity

“…Fermions coupled to emergent noncommutative gravity Daniela Klammer tation of tr E and R[ G] are equivalent 6 . After a rather lengthy computation, which can be found in [6], one yields the following compact form for the Ricci scalar in terms of the unimodular metric…”

“…After a rather lengthy computation, which can be found in [6], one yields the following compact form for the Ricci scalar in terms of the unimodular metric…”

“…Thus it is believed that these theories could play an important rôle on the way towards a quantum theory of gravity. Recently, a specific realization of this idea was published under the name of "emergent noncommutative gravity," see [4] and [5][6][7][8]. There, matrix models of noncommutative gauge theory describe dynamical noncommutative spaces.…”

Emergent Gravity and Gauge Theory From Matrix Models

“…On the other hand, Λ 4 is expected to be the scale of N = 4 SUSY breaking, since only N = 4 supersymmetric models do not induce this term 7,9 ; this is related to the lack of UV/IR mixing in these models as discussed below. This suggests that in order to have a finite gravitational coupling constant, the model should have N = 4 supersymmetry above a certain scale.…”