  In the present article, the authors intend to propose a new theory which
potentially allows the propagation of the formation and the evolution of
quarkonium in a thermal BIon. When quarks are close to each other, quarkonium
behaves like a scalar and by their getting away, it transits to a fermionic
system. In order to analyze this particular behaviour, a new outlook approach
needs to be adopted as the concurrent view is found deficient to analyse the
aforesaid behaviour. Therefore, the authors' post deliberation accept the
fermions and fermionic being cognate. We need to accept a theory that the
origin of fermions and bosons be the same. However, in $M$-theory, these
particles are independent and for this reason, \textbf{we use a new broader
theory based on Lie-$N$-Algebra and we call it BLNA (Broad Lie-$N$-Algebra)}
theory. Thus, the BLNA in a way the $M$-theory with $11$ dimensions. In this
model, two types of energies with opposite signs emerge from nothing such as
the sum over them becomes zero. They produce two types of branes with opposite
quantum numbers and bosonic fields, which interact with each other and get
compact. By compacting branes, the quarks and anti-quarks are produced on
branes and exchange the graviton and the gravitino. These particles produce two
types of wormholes which act opposite to each other. They preclude from closing
or getting away of branes from each other and also occurrence of confinement.
This confined potential which emerges from these wormholes depends on the
separation distance between quarks and anti-quarks and also on temperature of
system and is reduced to predicted potential in experiments and QCD. Also,
total entropy of this system grows with increasing temperature and produces a
repulsive force which leads to the separation of quarks and anti-quarks and
also to the emergence of deconfinement.
