PIRSA:15030076

Splitting processes of membranes in the pp-wave matrix model and three dimensional analog of Riemann surfaces

(2015). Splitting processes of membranes in the pp-wave matrix model and three dimensional analog of Riemann surfaces. Perimeter Institute. https://pirsa.org/15030076

Splitting processes of membranes in the pp-wave matrix model and three dimensional analog of Riemann surfaces. Perimeter Institute, Mar. 03, 2015, https://pirsa.org/15030076 

          @misc{ pirsa_PIRSA:15030076,
            doi = {10.48660/15030076},
            url = {https://pirsa.org/15030076},
            author = {},
            keywords = {Quantum Fields and Strings},
            language = {en},
            title = {Splitting processes of membranes in the pp-wave matrix model and three dimensional analog of Riemann surfaces},
            publisher = {Perimeter Institute},
            year = {2015},
            month = {mar},
            note = {PIRSA:15030076 see, \url{https://pirsa.org}}
          }
DOI 10.48660/15030076
Collection
Talk Type Scientific Series
Subject

Abstract

The talk will be based on a work in progress with Stefano Kovacs
(Dublin IAS) and Yuki Sato (Wits University). In a previous work
(arxiv:1310.0016) we have shown that,
in the M-theory regime (large N with the Chern-Simon level k fixed)
of the duality between ABJM theory and M-theory on AdS4 x S7/Zk,
certain monopole operators with large R charges on the gauge theory side
correspond to spherical membranes
(which is in general in non-BPS excited states) in the pp-wave matrix
model on the dual side.

Having in mind application to
the study of three point functions of the monopole operators
from the dual side, we study the BPS instanton equation
of the pp-wave matrix model. The instanton equation describes, for example,
a process in which a single spherical membrane splits into
two spherical membranes. Under a certain
approximation which is valid when the matrix size is large,
the instanton equation can be recast
into a three dimensional Laplace equation;
a time snapshot of the membrane configuration corresponds
to an equipotential surface of the solution of the Laplace equation.
In order to study the above mentioned splitting process,
we found that one has to introduce a special boundary condition
of the Laplace equation: one prepares two copies of
three dimensional space which are connected in a manner analogous
to Riemann surfaces. We will discuss an exact solution
of the Laplace equation under this boundary condition, and 
the corresponding instanton solution, in which a membrane splits into two.