Open topological defects and boundary RG flows

Konechny, Anatoly

doi:10.1088/1751-8121/ab7c8b

Cited by 9 publications

(6 citation statements)

References 26 publications

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“…In particular, boundaries of 2d CFTs form modules of the generalized fusion category symmetries in the bulk [80][81][82]. This is because when a TDL L a acts by fusion on a given boundary |B α , it produces another boundary |L a B α (possibly reducible) that obey all the bootstrap axioms thanks to the topological nature and locality properties of the TDLs.…”

Section: Boundaries From Fusion With Topological Defectsmentioning

confidence: 99%

Bootstrapping Boundaries and Branes

Collier¹,

Mazáč²,

Wang³

2021

Preprint

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The study of conformal boundary conditions for two-dimensional conformal field theories (CFTs) has a long history, ranging from the description of impurities in one-dimensional quantum chains to the formulation of D-branes in string theory. Nevertheless, the landscape of conformal boundaries is largely unknown, including in rational CFTs, where the local operator data is completely determined. We initiate a systematic bootstrap study of conformal boundaries in 2d CFTs by investigating the bootstrap equation that arises from the openclosed consistency condition of the annulus partition function with identical boundaries. We find that this deceivingly simple bootstrap equation, when combined with unitarity, leads to surprisingly strong constraints on admissible boundary states. In particular, we derive universal bounds on the tension (boundary entropy) of stable boundary conditions, which provide a rigorous diagnostic for potential D-brane decays. We also find unique solutions to the bootstrap problem of stable branes in a number of rational CFTs. Along the way, we observe a curious connection between the annulus bootstrap and the sphere packing problem, which is a natural extension of previous work on the modular bootstrap. We also derive bounds on the boundary entropy at large central charge. These potentially have implications for end-of-the-world branes in pure gravity on AdS 3 .

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Section: Boundaries From Fusion With Topological Defectsmentioning

confidence: 99%

Bootstrapping Boundaries and Branes

Collier¹,

Mazáč²,

Wang³

2021

Preprint

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“…As we will discuss at the end of section 4, the two boundary states |+ + |− and |free are related by Kramers-Wannier (KW) duality [47]. The interpretation of the linear superposition in terms of a topological defect [51,52] and its appearance along a boundary flow has also been recently emphasized in [53]. Finally notice that in principle other Z 2 symmetric linear superpositions of the fixed boundary states could appear in equation ( 9), leading to larger boundary entropies.…”

Section: Formation Probabilities and Boundary Entropies In The Xy Chainmentioning

confidence: 99%

Scaling of the formation probabilities and universal boundary entropies in the quantum XY spin chain

Ares¹,

Rajabpour²,

Viti³

2020

J. Stat. Mech.

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We calculate exactly the probability to find the ground state of the XY chain in a given spin configuration in the transverse σ z -basis. By determining finite-volume corrections to the probabilities for a wide variety of configurations, we obtain the universal boundary entropy at the critical point. The latter is a benchmark of the underlying boundary conformal field theory characterizing each quantum state. To determine the scaling of the probabilities, we prove a theorem that expresses, in a factorized form, the eigenvalues of a sub-matrix of a circulant matrix as functions of the eigenvalues of the original matrix. Finally, the boundary entropies are computed by exploiting a generalization of the Euler-MacLaurin formula to non-differentiable functions. It is shown that, in some cases, the spin configuration can flow to a linear superposition of Cardy states. Our methods and tools are rather generic and can be applied to all the periodic quantum chains which map to free-fermionic Hamiltonians.

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“…Boundaries from Fusion with topological defects. In particular, boundaries of 2d CFTs form modules of the generalized fusion category symmetries in the bulk [80][81][82]. This is because when a TDL L a acts by fusion on a given boundary |B α , it produces another boundary |L a B α (possibly reducible) that obey all the bootstrap axioms thanks to the topological nature and locality properties of the TDLs.…”

Section: Boundaries From Generalized Symmetriesmentioning

confidence: 99%

Bootstrapping boundaries and branes

Collier

Mazáč

Wang

2023

J. High Energ. Phys.

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The study of conformal boundary conditions for two-dimensional conformal field theories (CFTs) has a long history, ranging from the description of impurities in one-dimensional quantum chains to the formulation of D-branes in string theory. Nevertheless, the landscape of conformal boundaries is largely unknown, including in rational CFTs, where the local operator data is completely determined. We initiate a systematic bootstrap study of conformal boundaries in 2d CFTs by investigating the bootstrap equation that arises from the open-closed consistency condition of the annulus partition function with identical boundaries. We find that this deceivingly simple bootstrap equation, when combined with unitarity, leads to surprisingly strong constraints on admissible boundary states. In particular, we derive universal bounds on the tension (boundary entropy) of stable boundary conditions, which provide a rigorous diagnostic for potential D-brane decays. We also find unique solutions to the bootstrap problem of stable branes in a number of rational CFTs. Along the way, we observe a curious connection between the annulus bootstrap and the sphere packing problem, which is a natural extension of previous work on the modular bootstrap. We also derive bounds on the boundary entropy at large central charge. These potentially have implications for end-of-the-world branes in pure gravity on AdS3.

show abstract

Open topological defects and boundary RG flows

Cited by 9 publications

References 26 publications

Bootstrapping Boundaries and Branes

Bootstrapping Boundaries and Branes

Scaling of the formation probabilities and universal boundary entropies in the quantum XY spin chain

Bootstrapping boundaries and branes

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