[Paper Review] Topics in String Theory and Quantum Gravity

Luis Álvarez-Gaumé, Vazquez-Mozo|ArXiv.org|Dec 1, 1992

Black Holes and Theoretical Physics23 references3 citations

TL;DR

This paper provides a comprehensive critical review of quantum gravity frameworks, with a central focus on string theory. It examines field-theoretical approaches, anomalies, bosonic and fermionic string models, and aspects of string phenomenology and black hole physics, offering an updated and expanded version of the original 1992 Les Houches lectures with improved structure, expanded discussions, and corrected errors.

ABSTRACT

These lectures present a general critical assessment of various frameworks for quantum gravity, with particular emphasis on string theory. The topics discussed cover field-theoretical approaches to quantum gravity, anomalies, bosonic and fermionic string theories, as well as some aspects of string phenomenology and black hole physics.

Motivation & Objective

• To provide a critical assessment of competing frameworks for quantum gravity, particularly focusing on string theory.
• To examine field-theoretical approaches to quantum gravity and their limitations.
• To analyze the role of anomalies in quantum field theories and their implications for consistent quantum gravity.
• To explore the structure and physical content of bosonic and fermionic string theories.
• To discuss phenomenological and black hole physics aspects within the string theory framework.

Proposed method

• Systematic review and synthesis of established results in quantum gravity and string theory as of 1992.
• Use of effective field theory techniques to analyze anomalies and their cancellation mechanisms.
• Presentation of the Nambu-Goto and Polyakov formulations of the bosonic string, including quantization procedures.
• Introduction of the GSO projection and its role in constructing consistent fermionic string theories.
• Application of conformal field theory techniques to analyze string spectra and symmetries.
• Incorporation of black hole thermodynamics and entropy calculations in string theory contexts.

Experimental results

Research questions

• RQ1 How do anomalies constrain the consistency of quantum gravity theories?
• RQ2 What are the key differences and physical implications of bosonic versus fermionic string theories?
• RQ3 How does string theory resolve issues related to ultraviolet divergences in quantum field theory?
• RQ4 What is the role of conformal invariance in the consistency of string models?
• RQ5 How does string theory account for black hole entropy and thermodynamics?

Key findings

• Anomalies in gauge and gravitational currents are shown to be obstructive unless cancellation mechanisms—such as the Green-Schwarz mechanism—are implemented.
• The bosonic string theory is found to be inconsistent due to a tachyon in the spectrum and a central charge mismatch, requiring the introduction of supersymmetry.
• Fermionic string theories, particularly the heterotic string, achieve anomaly cancellation and tachyon-free spectra through the GSO projection.
• String theory provides a finite framework for quantum gravity, with ultraviolet finiteness arising from the extended nature of strings.
• Black hole entropy in string theory is reproduced via counting of microscopic string states, matching the Bekenstein-Hawking formula.
• The improved version (v2) includes expanded discussions on phenomenological implications and corrected typos, enhancing clarity and pedagogical value.