Effective mass and symmetry breaking in the Ishibashi-Kawai-Kitazawa-Tsuchiya matrix model from compactification

The Ishibashi-Kawai-Kitazawa-Tsuchiya (IKKT) model is a promising candidate for a nonperturbative description of type IIB superstring theory. It is known from analytic approaches and numerical simulations that the IKKT matrix model with a mass term admits interesting cosmological solutions. However, this mass term is often introduced by hand and serves as a regulator in the theory. In the present paper, we show that an effective mass matrix can arise naturally in the IKKT model by imposing a toroidal compactification where the space-time fermions acquire antiperiodic boundary conditions. When six spatial dimensions are chosen to be compact, the effective mass matrix breaks the SO(1,9) space-time symmetry of the IKKT model to <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi>SO</a:mi><a:mo stretchy="false">(</a:mo><a:mn>1</a:mn><a:mo>,</a:mo><a:mn>3</a:mn><a:mo stretchy="false">)</a:mo><a:mo stretchy="false">×</a:mo><a:mi>SO</a:mi><a:mo stretchy="false">(</a:mo><a:mn>6</a:mn><a:mo stretchy="false">)</a:mo></a:mrow></a:math>. This paves the way for space-time solutions of the IKKT model where SO(1,9) symmetry is naturally broken to <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:mrow><h:mi>SO</h:mi><h:mo stretchy="false">(</h:mo><h:mn>1</h:mn><h:mo>,</h:mo><h:mn>3</h:mn><h:mo stretchy="false">)</h:mo><h:mo stretchy="false">×</h:mo><h:mi>SO</h:mi><h:mo stretchy="false">(</h:mo><h:mn>6</h:mn><h:mo stretchy="false">)</h:mo></h:mrow></h:math>.