On the Spontaneous Breakdown of Lorentz Symmetry in Matrix Models of Superstrings

Abstract

In string or M theories, the spontaneous breaking of 10D or 11D Lorentz symmetry is required to describe our space-time. A direct approach to this issue is provided by the IIB matrix model. We study its 4D version, which corresponds to the zero volume limit of 4D super SU(N) Yang-Mills theory. Based on the moment of inertia as a criterion, spontaneous symmetry breaking (SSB) seems to occur, so that only one extended direction remains, as first observed by Bialas, Burda et al. However, using Wilson loops as probes of space-time we do not observe any sign of SSB in Monte Carlo simulations where N is as large as 48. This agrees with an earlier observation that the phase of the fermionic integral, which is absent in the 4D model, should play a crucial role if SSB of Lorentz symmetry really occurs in the 10D IIB matrix model.

arXiv comment16 pages, 5 figures, a few points are made more precise

References in corpus (28)

• An Alternative to Compactification
• M Theory As A Matrix Model: A Conjecture
• A Large-N Reduced Model as Superstring
• Space-Time Structures from IIB Matrix Model
• Monte Carlo Approach to M-Theory
• Dynamical Aspects of Large N Reduced Models
• IIB Matrix Model
• Monte Carlo Studies of the IIB Matrix Model at Large N
• Large N Dynamics of Dimensionally Reduced 4D SU(N) Super Yang-Mills Theory
• Spontaneous Breakdown of Lorentz Invariance in IIB Matrix Model
• Convergent Yang-Mills Matrix Theories
• String Field Theory from IIB Matrix Model
• Brane world from IIB matrices
• Finite Yang-Mills Integrals
• Eigenvalue Distributions in Yang-Mills Integrals
• String Scale in Noncommutative Yang-Mills
• The Convergence of Yang-Mills Integrals
• Geometry of Reduced Supersymmetric 4D Yang-Mills Integrals
• Gaussian and Mean Field Approximations for Reduced Yang-Mills Integrals
• Large N limit of the IKKT matrix model
• Space-Time and Matter in IIB Matrix Model - gauge symmetry and diffeomorphism -
• Simulating Simplified Versions of the IKKT Matrix Model
• Noncommutative String Worldsheets from Matrix Models
• Numerical Analysis of the Double Scaling Limit in the IIB Matrix Model
• Large N Structure of the IIB Matrix Model
• Monte Carlo Studies of the Dimensionally Reduced 4d SU(N) Super Yang-Mills Theory
• Numerical Analysis of the Double Scaling Limit in the bosonic part of the IIB Matrix Model
• Statistical Physics Approach to M-theory Integrals

Cited by in corpus (31)

• Emergence of a 4D World from Causal Quantum Gravity
• Dynamical Generation of Four-Dimensional Space-Time in the IIB Matrix Model
• Non-lattice simulation for supersymmetric gauge theories in one dimension
• A new approach to the complex-action problem and its application to a nonperturbative study of superstring theory
• Nonperturbative studies of fuzzy spheres in a matrix model with the Chern-Simons term
• A non-perturbative study of 4d U(1) non-commutative gauge theory -- the fate of one-loop instability
• Systematic study of the SO(10) symmetry breaking vacua in the matrix model for type IIB superstrings
• Exactly Solvable Matrix Models for the Dynamical Generation of Space-Time in Superstring Theory
• Dynamical aspects of the fuzzy CP${}^2$ in the large $N$ reduced model with a cubic term
• Perturbative versus nonperturbative dynamics of the fuzzy S^2*S^2
• A general approach to the sign problem - the factorization method with multiple observables
• Progress in the numerical studies of the type IIB matrix model
• Perturbative dynamics of fuzzy spheres at large N
• Impact of supersymmetry on the nonperturbative dynamics of fuzzy spheres
• Gaussian and Mean Field Approximations for Reduced 4D Supersymmetric Yang-Mills Integral
• Exact fuzzy sphere thermodynamics in matrix quantum mechanics
• Absence of a fuzzy $S^4$ phase in the dimensionally reduced 5d Yang-Mills-Chern-Simons model
• Rotational Symmetry Breaking in Multi-Matrix Models
• The index of the overlap Dirac operator on a discretized 2d non-commutative torus
• Convergence of the Gaussian Expansion Method in Dimensionally Reduced Yang-Mills Integrals
• Complex Langevin analysis of the spontaneous breaking of 10D rotational symmetry in the Euclidean IKKT matrix model
• Monte Carlo Studies of the GWW Phase Transition in Large-N Gauge Theories
• Improved Perturbation Method and its Application to the IIB Matrix Model
• Testing the Gaussian expansion method in exactly solvable matrix models
• Probability distribution of the index in gauge theory on 2d non-commutative geometry
• Adding a Myers Term to the IIB Matrix Model
• The Large N Reduction in Matrix Quantum Mechanics -- a Bridge between BFSS and IKKT --
• Exotic trees
• Polyakov Lines in Yang-Mills Matrix Models
• Lattice Superstring and Noncommutative Geometry
• Dynamical Compactification of Extra Dimensions in the Euclidean IKKT Matrix Model via Spontaneous Symmetry Breaking