[Paper Review] A Critique of Pure String Theory: Heterodox Opinions of Diverse Dimensions

T. Banks|ArXiv.org|Jun 9, 2003

Black Holes and Theoretical Physics45 references85 citations

TL;DR

This paper critiques mainstream string theory by arguing that a background-independent, Poincaré-invariant, supersymmetry-violating vacuum cannot exist in quantum gravity, proposing instead that cosmological supersymmetry breaking (CSB) explains why we observe no low-energy supersymmetry. It suggests that black hole dominance at high energies and the finite entropy of de Sitter space constrain the theory, leading to a critical scaling relation $ m_{3/2} \sim \Lambda^{1/4} $, and advocates for a non-Lagrangian, high-energy-dominated framework for quantum gravity.

ABSTRACT

I present a point of view about what M Theory is and how it is related to the real world, which departs in certain crucial respects from conventional wisdom. I argue against the possibility of a background independent formulation of the theory, or of a Poincare invariant, Supersymmetry violating vacuum state. A fundamental assumption is black hole dominance of high energy physics. Much of this paper is a compilation of things I have said elsewhere. I review a crude argument for the critical exponent connecting the gravitino mass and the cosmological constant, and propose a framework for finding a quantum theory of de Sitter space.

Motivation & Objective

• To challenge the conventional assumption that a Poincaré-invariant, supersymmetry-violating vacuum can exist in string theory.
• To argue that black hole dominance at high energies invalidates the standard perturbative approach to quantum gravity.
• To propose that cosmological supersymmetry breaking (CSB) naturally explains the absence of low-energy supersymmetry.
• To motivate a non-Lagrangian, high-energy-dominated framework for quantum gravity based on holography and dS entropy.
• To explore the feasibility of a quantum theory of de Sitter space and the critical scaling of gravitino mass with the cosmological constant.

Proposed method

• Proposes that the high-energy behavior of quantum gravity is governed by non-Gaussian fixed points, not Gaussian (Lagrangian) dynamics.
• Uses the holographic principle and black hole dominance to argue that the number of states in de Sitter space is finite, bounded by $ e^{10^{120}} $.
• Applies the Cartan-Penrose equation to connect local supersymmetry to the holographic principle.
• Introduces an infrared cutoff at $ R_{\text{dS}}^{1/2} $ in Planck units to address IR divergences in perturbative quantum gravity on de Sitter space.
• Analyzes loop corrections to the gravitino mass term, suggesting they may yield the anomalous scaling $ m_{3/2} \sim \Lambda^{1/4} $ due to the dS radius as an IR regulator.
• Proposes searching for an algorithm to compute the superpotential on moduli space for $ \mathcal{N}=1, d=4 $ SUSic compactifications of M-theory, including isolated vacua.

Experimental results

Research questions

• RQ1 Can a background-independent, Poincaré-invariant, supersymmetry-violating vacuum exist in quantum gravity?
• RQ2 What is the origin of the critical scaling $ m_{3/2} \sim \Lambda^{1/4} $, and can it be derived from a quantum theory of de Sitter space?
• RQ3 Is there a consistent quantum theory of de Sitter space that avoids IR divergences in perturbative gravity?
• RQ4 Can cosmological supersymmetry breaking (CSB) explain the absence of low-energy supersymmetry in nature?
• RQ5 Is there a non-perturbative algorithm to compute the superpotential on moduli space for $ \mathcal{N}=1, d=4 $ SUSic M-theory compactifications?

Key findings

• The paper argues that no consistent, supersymmetry-violating, Poincaré-invariant vacuum can exist in quantum gravity due to black hole dominance and the finite entropy of de Sitter space.
• It proposes that the gravitino mass scales with the cosmological constant as $ m_{3/2} \sim \Lambda^{1/4} $, motivated by IR divergences regulated by the dS radius.
• The number of states in the real universe is finite, bounded by $ e^{10^{120}} $, implying that low-energy physics is only approximately Poincaré-invariant.
• The limiting vacuum—defined as the Poincaré-invariant approximation to the real world—must be four-dimensional, $ \mathcal{N}=1 $ supersymmetric, and possess an exact complex R symmetry.
• The paper suggests that the absence of SUSY-violating quantum gravity in asymptotically flat space is not accidental, and conjectures that no such theory exists.
• It proposes that the search for a non-perturbative formulation of M-theory may be guided by computing the superpotential on moduli space and finding stationary points where it vanishes.