Defect Conformal Manifolds from Phantom Noninvertible Symmetries

Area of Science:

• Condensed matter theory
• Quantum field theory
• String theory

Background:

• Conformal Field Theories (CFTs) in (1+1) dimensions are crucial for understanding critical phenomena.
• Interface conformal manifolds are important for studying defects and boundaries in quantum systems.
• Symmetry and supersymmetry often play key roles in simplifying CFT analysis.

Purpose of the Study:

• To explore a general mechanism for generating interesting interface conformal manifolds in (1+1)d CFTs.
• To investigate these phenomena in the absence of continuous internal symmetry or supersymmetry.
• To demonstrate the utility of a symmetry-based approach for analyzing defect conformal manifolds.

Main Methods:

• Analyzing (1+1)d CFTs with a focus on folded theories.
• Identifying and studying enhanced, generically noninvertible symmetries.
• Utilizing symmetry breaking mechanisms to generate interface conformal manifolds.
• Computing the evolution of the reflection coefficient along the defect conformal manifold.

Main Results:

• A general mechanism enabling interesting interface conformal manifolds in (1+1)d CFTs without continuous symmetry or supersymmetry has been identified.
• The breaking of an enhanced, noninvertible symmetry in the folded theory is key to this mechanism.
• The symmetry-based approach allows for the computation of the reflection coefficient's evolution.

Conclusions:

• The study provides a novel mechanism for constructing interface conformal manifolds in CFTs.
• The findings highlight the importance of noninvertible symmetries in quantum field theory.
• The approach is extendable to higher dimensions and offers insights into no-go theorems.