Generalized uncertainty principle as a consequence of the effective field theory

Abstract

We will demonstrate that the generalized uncertainty principle exists because of the derivative expansion in the effective field theories. This is because in the framework of the effective field theories, the minimum measurable length scale has to be integrated away to obtain the low energy effective action. We will analyze the deformation of a massive free scalar field theory by the generalized uncertainty principle, and demonstrate that the minimum measurable length scale corresponds to a second more massive scale in the theory, which has been integrated away. We will also analyze CFT operators dual to this deformed scalar field theory, and observe that scaling of the new CFT operators indicates that they are dual to this more massive scale in the theory. We will use holographic renormalization to explicitly calculate the renormalized boundary action with counter terms for this scalar field theory deformed by generalized uncertainty principle, and show that the generalized uncertainty principle contributes to the matter conformal anomaly.

Minimal length effects on chaotic motion of particles around black hole horizon

“…However in a holographic framework, it is tempting to find how the corrections due to the minimal length in bulk changes the bound (42). Note that higher derivative corrections due to the minimal length for a scalar field theory in AdS space was analyzed and related to the conformal field theory on the boundary in [48].…”

Minimal length effect on the broadening of free wave packets and its physical implications

“…This consideration is in line with the very definition of the GUP commutator (20) which is an approximate expression up to quadratic powers. The new variables in (27) are defined as…”

“…It is straightforward, once again, to write down a solution of (27), under the assumption that the initial wavepacket is minimal (ξ(t 0 ) = 0). The resulting equation is…”

“…On the other hand there is a growing consensus that, inspired by certain quantum gravity theories, are advocating about the existence of a fundamental minimal length scale (at the Planck length). Among them, studies in string theory [2][3][4][5][6][7][8], Doubly Special Relativity [9][10][11][12], black hole physics [13][14][15], Loop Quantum Gravity (LQG) [16,17], non-commutative quantum geometries [18][19][20] and more general approaches concerning QM and General Relativity [21][22][23][24][25][26][27][28][29][30] manifest this existence of a minimal length by replacing the HUP by a Generalized Uncertainty Principle (GUP) whose exact form, however, often disagrees among various proposals (for a broad overview see [7,13,[31][32][33][34][35] and references therein). The GUP based approaches have a motivation to provide a short hand exercise in the search for quantum gravity effects, hypothesized to be realized in the form a minimal length, in low energy physics and, if it is indeed found then ask for an appropriate fundamental theory, from first principles, to explain this effective description of physical reality [36] (which may well be one of the existing theories -LQG or string theory or an entirely new theory).…”

Black hole complementarity with the generalized uncertainty principle in Gravity's Rainbow

“…It could be derived from not only general considerations of quantum mechanics and gravity [12] but also string theory [13][14][15][16], which gives rise to a minimal length of the order of the Planck length, (∆X) min ∼ √ α GUP L P . Many efforts have been devoted to studying various aspects of the GUP [17][18][19][20][21][22][23][24]. Especially, the role of GUP was discussed in the context of the information loss problem [25].…”