$\beta$-deformation for matrix model of M-theory

Abstract

A new class of deformation of the matrix model of M-theory is considered. The deformation is analogous to the so-called $\b$-deformation of $D=3+1$, $\mN=4$ Super Yang-Mills theory, which preserves the conformal symmetry. It is shown that the deformed matrix model can be considered as a matrix model of M-theory on a certain curved background in eleven-dimensional supergravity, under a scaling limit involving the deformation parameter and $N$ (the size of the matrices). The background belongs to the so-called pp-wave type metric with a non-constant four-form flux depending linearly on transverse coordinates. Some stable solutions of the deformed model are studied, which correspond to membranes with the torus topology. In particular, it is found that apparently distinct configurations of membranes, having different winding numbers, are indistinguishable in the matrix model. Simultaneous introduction of both $\b$-deformation and mass-deformation is also considered, and, in particular, a situation is found in which the stable membrane configuration interpolates between a torus and a sphere, depending on the values of the deformation parameters.

36 pages

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Cited by in corpus (9)

• An N=1 Superfield Action for M2 branes
• Classification of the BPS states in Bagger-Lambert Theory
• Matrix embeddings on flat $R^3$ and the geometry of membranes
• Topological branes, p-algebras and generalized Nahm equations
• On Matrix Model Formulations of Noncommutative Yang-Mills Theories
• Membranes from monopole operators in ABJM theory: large angular momentum and M-theoretic AdS_4/CFT_3
• Loop equations and topological recursion for the arbitrary-$\beta$ two-matrix model
• Curved Space (Matrix) Membranes
• M-theory on pp-waves with a holomorphic superpotential and its membrane and matrix descriptions