Measure of the potential valleys of the supermembrane theory

Lyonell Boulton, María Pilar García Del Moral, Álvaro Restuccia

Research output: Contribution to journalArticle

4 Downloads (Pure)

Abstract

We analyse the measure of the regularized matrix model of the supersymmetric potential valleys, Ω, 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 Ω 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 1,2(Ω) onto L 2(Ω). 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.

Original languageEnglish
Article number134873
JournalPhysics Letters B
Volume797
Early online date21 Aug 2019
DOIs
Publication statusPublished - 10 Oct 2019

ASJC Scopus subject areas

  • Nuclear and High Energy Physics

Fingerprint Dive into the research topics of 'Measure of the potential valleys of the supermembrane theory'. Together they form a unique fingerprint.

  • Cite this