On the classification of duality defects in $c=2$ compact boson CFTs with a discrete group orbifold

Abstract

We propose a novel approach to exploring duality defects in the $c=2$ compact boson conformal field theory (CFT). This study is motivated by the desire to classify categorical symmetries, particularly duality defects, in CFTs. While the $c=1$ case has been extensively studied, and the types of realizable duality defects are largely understood, the situation becomes significantly more complex for $c=2$. The simplicity of the $c=1$ case arises from the fact that its theory is essentially determined by the radius of compactification. In contrast, the $c=2$ case involves more parameters, leading to a more intricate action of T-duality. As a result, directly solving the condition for a theory to be self-dual under orbifolding becomes highly challenging. To address this, we categorize duality defects into four types and demonstrate that the condition for a toroidal branch theory to be self-dual under an orbifold induced by an automorphism generated by shift symmetry can be reformulated as quadratic equations. We also found that for ``almost all" theories we can enumerate all solutions for such equations. Moreover, this reformulation enables the simultaneous exploration of multiple duality defects and provides evidence for the existence of duality defects under specific parameter families for the theory, such as $(\tau ,\rho )=(it,\frac{1}{2}+it)$ where $t\in \mathbb{Q}$.

31 pages, 2 figures

References in corpus (17)

• Generalized Global Symmetries
• TFT construction of RCFT correlators I: Partition functions
• Duality and defects in rational conformal field theory
• Non-Invertible Duality Defects in 3+1 Dimensions
• Defect lines, dualities, and generalised orbifolds
• Topological defects for the free boson CFT
• Tunneling in Quantum Wires: a Boundary Conformal Field Theory Approach
• Reflection and Transmission for Conformal Defects
• TFT construction of RCFT correlators IV: Structure constants and correlation functions
• TFT construction of RCFT correlators II: Unoriented world sheets
• Defect Lines in the Ising Model and Boundary States on Orbifolds
• Simple currents versus orbifolds with discrete torsion -- a complete classification
• Rational Conformal Field Theories and Complex Multiplication
• Classification of symmetric toroidal orbifolds
• Boundaries, defects and Frobenius algebras
• Crystallographic Orbifolds: Towards a Classification of Unitary Conformal Field Theories with Central Charge c = 2
• Non-Invertible T-duality at Any Radius via Non-Compact SymTFT

Cited by in corpus (1)

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