Dynamical generation of non-Abelian gauge group via the improved perturbation theory

We construct a class of matrix models, where supersymmetry (SUSY) is spontaneously broken at the matrix size N infinite. The models are obtained by dimensional reduction of matrix-valued SUSY quantum mechanics. The potential of the models is slowly varying, and the large-N limit is taken with the slowly varying limit.First, we explain our formalism, introducing an external field to detect spontaneous SUSY breaking, analogously to ordinary (bosonic) symmetry breaking. It is observed that SUSY is possibly broken even in systems in less than one-dimension, for example, discretized quantum mechanics with a finite number of discretized time steps. Then, we consider spontaneous SUSY breaking in the SUSY matrix models with slowly varying potential, where the external field is turned off after the large-N and slowly varying limit, analogously to the thermodynamic limit in statistical systems. On the other hand, without taking the slowly varying limit, in the SUSY matrix model with a double-well potential whose SUSY is broken due to instantons for finite N , a number of supersymmetric behavior is explicitly seen at large N . It convinces us that the instanton effect disappears and the SUSY gets restored in the large-N limit.

Section: Summary and Discussionmentioning

confidence: 99%

Spontaneous supersymmetry breaking in large-N matrix models with slowly varying potential

Kuroki

Sugino

2010

“…Finally, we hope that similar analysis for super Yang-Mills matrix models [2,3,4], which have been proposed as nonperturbative definitions of superstring/M theories, will shed light on new aspects of spontaneous SUSY breaking in superstring/M theories. To carry out the analysis, the method of the Gaussian expansion or improved perturbation theory would be useful [26,5,27,28,29].…”

Section: Summary and Discussionmentioning

confidence: 99%

Spontaneous supersymmetry breaking in matrix models from the viewpoints of localization and Nicolai mapping

Kuroki

Sugino

2011

In the previous work, it was shown that, in supersymmetric (matrix) discretized quantum mechanics, inclusion of an external field twisting the boundary condition of fermions enables us to discuss spontaneous breaking of supersymmetry (SUSY) in the path-integral formalism in a well-defined way. In the present work, we continue investigating the same systems from the points of view of localization and Nicolai mapping. The localization is studied by changing of integration variables in the path integral, which is applicable whether or not SUSY is explicitly broken. We examine in detail how the integrand of the partition function with respect to the integral over the auxiliary field behaves as the auxiliary field vanishes, which clarifies a mechanism of the localization. In SUSY matrix models, we obtain a matrix-model generalization of the localization formula. In terms of eigenvalues of matrix variables, we observe that eigenvalues' dynamics is governed by balance of attractive force from the localization and repulsive force from the Vandermonde determinant. The approach of the Nicolai mapping works even in the presence of the external field. It enables us to compute the partition function of SUSY matrix models for finite N (N is the rank of matrices) with arbitrary superpotential at least in the leading nontrivial order of an expansion with respect to the small external field. We confirm the restoration of SUSY in the large-N limit of a SUSY matrix model with a double-well scalar potential observed in the previous work.

“…which are nothing but the equations of motion for the metric tensor and the B-field 12 . Note that we could set V a = 0 and L abc = 0 in this case while it is not the case when the mass term is absent.…”

Section: Matrix Model With Mass Termmentioning

confidence: 99%

“…In[12], this model was studied further by using the improved perturbation theory, and it was argued that this vacuum is indeed the nonperturbative one.…”

mentioning

confidence: 99%

Field equations of massless fields in the new interpretation of the matrix model

Furuta¹,

Hanada²,

Kawai³

et al. 2007

Recently, some of the authors have introduced a new interpretation of matrix models in which covariant derivatives on any curved space can be expressed by large-N matrices. It has been shown that the Einstein equation follows from the equation of motion of IIB matrix model in this interpretation. In this paper, we generalize this argument to covariant derivatives with torsion. We find that some components of the torsion field can be identified with the dilaton and the B-field in string theory. However, the other components do not seem to have string theory counterparts. We also consider the matrix model with a mass term or a cubic term, in which the equation of motion of string theory is exactly satisfied.