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Chiral scale and conformal invariance in 2D quantum field theory
Diego M Hofman1, Andrew Strominger
1Center for the Fundamental Laws of Nature, Harvard University, Cambridge, Massachusetts 02138, USA.
Physical Review Letters
|November 24, 2011
Summary
A 2D quantum field theory with only left scaling symmetry implies left conformal symmetry. Right translations are enhanced to either right conformal symmetry or a U(1) Kac-Moody symmetry, expanding conformal field theory understanding.
Area of Science:
- Quantum Field Theory
- Conformal Field Theory
- Theoretical Physics
Background:
- Local, unitary, Poincaré-invariant 2D quantum field theories with scaling symmetry possess left and right conformal symmetry.
- Previous work established a link between scaling symmetry and conformal symmetry in 2D quantum field theories.
Purpose of the Study:
- To investigate the implications of a chiral scenario in 2D quantum field theory, starting with only a left global scaling symmetry.
- To determine the resulting symmetries when Lorentz invariance is not assumed.
Main Methods:
- Analysis of a chiral 2D quantum field theory model.
- Exploring the consequences of a left global scaling symmetry without assuming Lorentz invariance.
Main Results:
- A left conformal symmetry is necessarily implied.
- Right translations are shown to enhance to either a right conformal symmetry or a left U(1) Kac-Moody symmetry.
Conclusions:
- The study reveals that even with reduced initial symmetries, conformal symmetry is robust in 2D quantum field theories.
- The findings offer new insights into the structure of symmetries in chiral conformal field theories.
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