Unravelling the Holomorphic Twist: Central Charges

Area of Science:

• Supersymmetric quantum field theory
• High-energy physics
• Theoretical physics

Background:

• The holomorphic twist is a key technique for analyzing minimally protected sectors in supersymmetric quantum field theories.
• Understanding the algebraic structures of these theories is crucial for uncovering their fundamental properties.

Purpose of the Study:

• To investigate the algebraic structure of the holomorphic twist in four-dimensional superconformal field theories.
• To explore the enhancement of flavour and conformal symmetry algebras.
• To relate binary and ternary brackets to infinite-dimensional symmetry algebras.

Main Methods:

• Applying the holomorphic twist to four-dimensional superconformal field theories.
• Explicitly computing binary and ternary brackets.
• Analyzing the relationship between these brackets and infinite-dimensional symmetry algebras.

Main Results:

• Flavour and conformal symmetry algebras are enhanced to infinite-dimensional higher Kac-Moody and higher Virasoro algebras.
• Central extensions of these enhanced algebras precisely encode conformal anomalies (a and c) and flavour central charges.
• This finding parallels the known relationship between the conformal anomaly c and the Virasoro algebra central extension in two dimensions.

Conclusions:

• The study demonstrates a powerful connection between algebraic structures (brackets and central extensions) and physical observables (anomalies and charges) in supersymmetric field theories.
• The findings provide new insights into the structure of four-dimensional superconformal field theories and the role of the holomorphic twist.
• This work offers a framework for further investigations into anomalies and symmetries in quantum field theory.