Quaternions and M(atrix) theory in spaces with boundaries

Abstract

A proposal for the matrix model formulation of the M-theory on a space with a boundary is given. A general machinery for modding out a symmetry in M(atrix) theory is used for a Z_2 symmetry changing the sign of the X_1 coordinate. The construction causes the elements of matrices to be equivalent to real numbers or quaternions and the symmetry U(2N) of the original model is reduced to O(2N) or USp(2N)=U(N,H). We also show that membranes end on the boundary of the spacetime correctly in this construction.

plain LaTeX, 15 pages, 1st revision: references, school info and notes added (real matrix case, Mobius membranes and so on...) 2nd revision: notes on originators of ideas

References in corpus (1)

• Proposals on nonperturbative superstring interactions

Cited by in corpus (14)

• M(atrix) Theory: Matrix Quantum Mechanics as a Fundamental Theory
• Towards a Noncommutative Geometric Approach to Matrix Compactification
• Equations of the (2,0) Theory and Knitted Fivebranes
• Matrix Regularization of an Open Supermembrane ---towards M-theory five-branes via open supermembranes ---
• CPT and Other Symmetries in String/M Theory
• A Matrix Model for Heterotic $Spin(32)/Z_2$ and Type I String Theory
• A note on T^5/Z_2 compactification of the M-theory matrix model
• On Second-Quantized Open Superstring Theory
• On The M(atrix)-Model For M-Theory On $T^6$
• Universal Calabi-Yau Algebra: Towards an Unification of Complex Geometry
• Matrix Compactification On Orientifolds
• Matrix Orientifolding and Models with Four or Eight Supercharges
• Nonperturbative Formulations of Superstring Theory
• Orientifolded Matrices and Supersymmetries that Give Rise to Spacetime Directional Asymmetry of Effective Interactions