Measure of the potential valleys of the supermembrane theory

Boulton L.; García del Moral M.P.; Restuccia Á.

Abstract

We analyse the measure of the regularized matrix model of the supersymmetric potential valleys, Omega, of the Hamiltonian of non zero modes of supermembrane theory. This is the same as the Hamiltonian of the BFSS matrix model. We find sufficient conditions for this measure to be finite, in terms of the spacetime dimension. For SU(2) we show that the measure of Omega is finite for the regularized supermembrane matrix model when the transverse dimensions in the light cone gauge d = D - 2 >= 5. This covers the important case of seven and eleven dimensional supermembrane theories, and implies the compact embedding of the Sobolev space H-1,H-2(Omega) onto L-2(Omega). The latter is a main step towards the confirmation of the existence and uniqueness of ground state solutions of the outer Dirichlet problem for the Hamiltonian of the SU(N) regularized D = 11 supermembrane, and might eventually allow patching with the inner solutions. (C) 2019 Published by Elsevier B.V.

Más información

Título según WOS: Measure of the potential valleys of the supermembrane theory
Título según SCOPUS: Measure of the potential valleys of the supermembrane theory
Título de la Revista: PHYSICS LETTERS B
Volumen: 797
Editorial: ELSEVIER SCIENCE BV
Fecha de publicación: 2019
Idioma: English
DOI:

10.1016/j.physletb.2019.134873

Notas: ISI, SCOPUS