The Three Dimensional Dual of 4D Chirality

TL;DR

This paper explores the duality between 4D chiral gauge theories in Anti de Sitter space and 3D conformal field theories, revealing how boundary conditions induce symmetry breaking and anomalies.

Contribution

It identifies the 3D dual of 4D chiral symmetry breaking as a specific double-trace deformation in the dual CFT, linking boundary conditions to anomalous Ward identities.

Findings

Boundary conditions break chiral symmetry in 4D AdS theories.

The 3D dual involves a double-trace deformation of the CFT.

The dual deformation reproduces the 4D anomaly structure.

Abstract

Chiral gauge theories can be defined in four-dimensional Anti de Sitter space, but AdS boundary conditions explicitly break the chiral symmetry in a specific, well defined manner, which in turns results in an anomalous Ward identity. When the 4D theory admits a dual description in terms of a 3D CFT, the 3D dual of the broken chiral symmetry is a certain double-trace deformation of the CFT, which produces the same anomalous chiral Ward identities that obtains in the 4D bulk theory.