Spontaneous breakdown of Lorentz invariance in IIB matrix model

Abstract

We study the IIB matrix model, which is conjectured to be a nonperturbative definition of superstring theory, by introducing an integer deformation parameter ν which couples to the imaginary part of the effective action induced by fermions. The deformed IIB matrix model continues to be well-defined for arbitrary ν, and it preserves gauge invariance, Lorentz invariance, and the cluster property. We study the model at ν = ∞ using a saddle-point analysis, and show that ten-dimensional Lorentz invariance is spontaneously broken at least down to an eight-dimensional one. We argue that it is likely that the remaining eight-dimensional Lorentz invariance is further broken, which can be checked by integrating over the saddle-point configurations using standard Monte Carlo simulation.

Rotational symmetry breaking in multimatrix models

“…Of course this does not prevent other real-action multi-matrix models having different patterns of spontaneous symmetry breaking, nor does not say anything about the rôle played by a possible complex term in the action. For all these reasons our findings do not contradict the analysis of [69,70,71,72,73,74,77,82,83]. It would be interesting to carry out the analysis contained in this paper to an extended version of the model where the coupling constantsα are allowed to be complex numbers.…”

New approach to the complex-action problem and its application to a nonperturbative study of superstring theory

“…The factor Z f [A] represents the quantity obtained by integration over the fermionic matrices, and its explicit form is given for example in Refs. [7,11]. The convergence of the integral (1) for arbitrary N ≥ 2 was first conjectured [12] and proved recently [13].…”

“…The fermion integral Z f [A] in the partition function (1) is complex in general for D = 10, N ≥ 4 and for D = 6, N ≥ 3 [7]. Let us restrict ourselves to these cases in what follows.…”

Matrix models: fermion doubling versus anomaly

“…In fact, there is a no-go theorem due to Nielsen and Ninomiya [11,12], which states that the doubling cannot be avoided unless the gauge, Lorentz or other relevant symmetry is destroyed in the continuum limit. While the gauge symmetry plays the crucial rôle in the consistency of the model, breaking of the Lorentz symmetry is not dangerous for the model and maybe even desirable as a mechanism of spontaneous breaking of the ten dimensional Lorentz group to a lower dimensional one, [13].…”