Why Don't We Have a Covariant Superstring Field Theory?

TL;DR

This paper reviews the longstanding challenge of developing a covariant quantum superstring theory with manifest Lorentz and supersymmetry, analyzing various quantization methods and their algebraic structures, and highlighting unresolved issues.

Contribution

It provides a comprehensive review of different covariant quantization approaches for superstrings, emphasizing twistorial variables and their algebraic frameworks, and identifies key open problems.

Findings

Twistorial approaches offer promising algebraic structures for covariant superstring quantization.

Several quantization methods have distinct advantages and disadvantages.

Unsolved problems remain in achieving a fully consistent covariant superstring theory.

Abstract

This talk deals with the old problem of formulatingn a covariant quantum theory of superstrings, ``covariant'' here meaning having manifest Lorentz symmetry and supersymmetry. The advantages and disadvantages of several quantization methods are reviewed. Special emphasis is put on the approaches using twistorial variables, and the algebraic structures of these. Some unsolved problems are identified.