On membrane interactions and a three-dimensional analog of Riemann surfaces

Abstract

Membranes in M-theory are expected to interact via splitting and joining processes. We study these effects in the pp-wave matrix model, in which they are associated with transitions between states in sectors built on vacua with different numbers of membranes. Transition amplitudes between such states receive contributions from BPS instanton configurations interpolating between the different vacua. Various properties of the moduli space of BPS instantons are known, but there are very few known examples of explicit solutions. We present a new approach to the construction of instanton solutions interpolating between states containing arbitrary numbers of membranes, based on a continuum approximation valid for matrices of large size. The proposed scheme uses functions on a two-dimensional space to approximate matrices and it relies on the same ideas behind the matrix regularisation of membrane degrees of freedom in M-theory. We show that the BPS instanton equations have a continuum counterpart which can be mapped to the three-dimensional Laplace equation through a sequence of changes of variables. A description of configurations corresponding to membrane splitting/joining processes can be given in terms of solutions to the Laplace equation in a three-dimensional analog of a Riemann surface, consisting of multiple copies of R^3 connected via a generalisation of branch cuts. We discuss various general features of our proposal and we also present explicit analytic solutions.

64 pages, 17 figures. V2: An appendix, a figure and references added; various minor changes and improvements

References in corpus (5)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• On the CFT Operator Spectrum at Large Global Charge
• Instanton Operators in Five-Dimensional Gauge Theories
• Impurity Non-Preserving 3-Point Correlators of BMN Operators from PP-Wave Holography II : Fermionic Excitations
• On the singlet projector and the monodromy relation for psu(2, 2|4) spin chains and reduction to subsectors

Cited by in corpus (5)

• Spherical transverse M5-branes from the plane wave matrix model
• Giant graviton interactions and M2-branes ending on multiple M5-branes
• Towards a tensionless string field theory for the N=(2,0) CFT in d=6
• Cascade of instabilities in the classical limit of the BMN matrix model
• Turbulent aspects of BMN membrane dynamics