# Birth of the GUP and its effect on the entropy of the Universe in Lie-$N$-algebra

## TL;DR

This paper explores how the generalized uncertainty principle (GUP) arises in a novel Lie-$N$-algebra-based theory, affecting the entropy of the universe through brane interactions and higher-order derivatives.

## Contribution

It introduces GLNA-theory, a new framework unifying GUP origin with brane dynamics in higher-dimensional Lie-$N$-algebra models, extending M-theory.

## Key findings

- GUP for bosons and fermions emerges from brane interactions.
- Higher derivatives and timing dimensions modify the brane entropy.
- The theory reduces to M-theory with specific parameters.

## Abstract

In this paper, the origin of the generalized uncertainty principle (GUP) in an $M$-dimensional theory with Lie-$N$-algebra is considered. This theory which we name GLNA(Generalized Lie-$N$-Algebra)-theory can be reduced to $M$-theory with $M=11$ and $N=3$. In this theory, at the beginning, two energies with positive and negative signs are created from nothing and produce two types of branes with opposite quantum numbers and different numbers of timing dimensions. Coincidence with the birth of these branes, various derivatives of bosonic fields emerge in the action of the system which produce the $r$ GUP for bosons. These branes interact with each other, compact and various derivatives of spinor fields appear in the action of the system which leads to the creation of the GUP for fermions. The previous predicted entropy of branes in the GUP is corrected as due to the emergence of higher orders of derivatives and different number of timing dimensions.