Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv : The Spectrum of Boundary States in Symmetric Orbifolds

Alexandre Belin, James Sully, Shovon Biswas

Published Oct 11, 2021• 0 citations
OpenAlex

Abstract

We give an explicit construction of the complete set of Cardy boundary states that respect the extended chiral algebra for symmetric product orbifolds. The states are labelled by a choice of seed theory boundary states as well as a choice of representations of the symmetric group. At large $N$, we analyze the BCFT data which is relevant for holography, namely the boundary entropy and the one-point functions of single-trace operators. In some cases, typical boundary states are compatible with a bulk description in terms of an End-of-the-World brane along with backreacted matter fields. We discuss the significance of these results for the AdS/BCFT correspondence.

Related papers

States, symmetries and correlators of $T\bar{T}$ and $ J\bar{T} $ symmetric orbifolds

Soumangsu Chakraborty, Silvia Georgescu, Monica Guica

We derive various properties of symmetric product orbifolds of T\bar T T T ‾ and J\bar T J T ‾ - deformed CFTs from a field-theoretical perspective. First, we generalise the known formula for the torus partition function of a symmetric orbifold theory in terms of the one of the seed to non-conformal two-dimensional QFTs; specialising this to seed T\bar T T T ‾ and J\bar T J T ‾ - deformed CFTs reproduces previous results in the literature. Second, we show that the single-trace T\bar T T T ‾ and J\bar T J T ‾ deformations preserve the Virasoro and Kac-Moody symmetries of the undeformed symmetric product orbifold CFT, including their fractional counterparts, as well as the KdV charges. Finally, we discuss correlation functions in these theories. By extending a previously-proposed basis of operators for J\bar T J T ‾ - deformed CFTs to the single-trace case, we explicitly compute the correlation functions of both untwisted and twisted-sector operators and compare them to an appropriate set of holographic correlators. Our derivations are based mainly on Hilbert space techniques and completely avoid the use of conformal invariance, which is not present in these models.

arXiv:2306.16454•SciPost Physics•Jan 10, 2024•14 citations

Conformal and fractional boundary states in the symmetric orbifold of the level one SU(2) WZW model

Atsushi Yamaguchi

We study the space of the allowed boundary states in a particular c=1 conformal field theory, the symmetric orbifold of the level one SU(2) WZW model, where the orbifolding group G is a generic binary finite subgroup of SU(2). We especially construct generic boundary states in the orbifold, which can be extended from the Cardy states decomposed into Virasoro Ishibashi states. Our result involves conformal boundary states parameterized by the quotient SU(2)/G, and the fractional boundary states sitting at every fixed-point in the quotient. We find also that a conformal boundary state at a fixed-point in the quotient becomes a linear combination of the fractional boundary states sitting at the fixed-point. To be complete, we check the mutual consistency among all the boundary states we construct.

•Sep 10, 2003•0 citations

Bridging boundaries: $$ T\overline{T} $$, double holography, and reflected entropy

Debarshi Basu, Himanshu Chourasiya, Ankur Dey +1 more

A bstract We investigate the reflected entropy for bipartite mixed state configurations in a $$ T\overline{T} $$ T T ¯ deformed boundary conformal field theory in 2 dimensions (BCFT 2 ). The bulk dual is described by asymptotically AdS 3 geometries with the cut off surface pushed deeper into the bulk and truncated by an end of the world brane. We obtain the reflected entropy up to a linear order in the radial cut-off for static and time dependent configurations involving an eternal black hole, from the island and defect extremal surface (DES) prescriptions in the context of the deformed AdS/BCFT. We observe agreement of the leading order correction for all cases between the two prescriptions. We also obtain the analogous of the Page curves for the reflected entropy and investigate the modification due to the $$ T\overline{T} $$ T T ¯ deformation.

arXiv:2411.12827•Journal of High Energy Physics•Jun 17, 2025•6 citations

Symmetry Breaking Boundary States and Defect Lines

Thomas Quella, Volker Schomerus

We present a large and universal class of new boundary states which break part of the chiral symmetry in the underlying bulk theory. Our formulas are based on coset constructions and they can be regarded as a non-abelian generalization of the ideas that were used by Maldacena, Moore and Seiberg to build new boundary states for SU(N). We apply our expressions to construct defect lines joining two conformal field theories with possibly different central charge. Such defects can occur e.g. in the AdS/CFT correspondence when branes extend to the boundary of the AdS-space.

•Jan 1, 2002•77 citations

On the boundary conformal field theory approach to symmetry-resolved entanglement

Giuseppe Di Giulio, René Meyer, Christian Northe +2 more

We study the symmetry resolution of the entanglement entropy of an interval in two-dimensional conformal field theories (CFTs), by relating the bipartition to the geometry of an annulus with conformal boundary conditions. In the presence of extended symmetries such as Kac-Moody type current algebrae, symmetry resolution is possible only if the boundary conditions on the annulus preserve part of the symmetry group, i.e. if the factorization map associated with the spatial bipartition is compatible with the symmetry in question. The partition function of the boundary CFT (BCFT) is then decomposed in terms of the characters of the irreducible representations of the symmetry group preserved by the boundary conditions. We demonstrate that this decomposition already provides the symmetry resolution of the entanglement spectrum of the corresponding bipartition. Considering the various terms of the partition function associated with the same representation, or charge sector, the symmetry-resolved Rényi entropies can be derived to all orders in the UV cutoff expansion without the need to compute the charged moments. We apply this idea to the theory of a free massless boson with U(1) U ( 1 ) , \mathbb{R} ℝ and \mathbb{Z}_2 ℤ 2 symmetry.

arXiv:2212.09767•SciPost Physics Core•Jul 11, 2023•33 citations

Boundary States of c=1 and 3/2 Rational Conformal Field Theories

Andrea Cappelli A, Giuseppe D’Appollonio

We study the boundary states for the rational points in the moduli spaces of c=1 conformal and c=3/2 superconformal field theories, including the isolated Ginsparg points. We use the orbifold and simple-current techniques to relate the boundary states of different theories and to obtain symmetry-breaking, non-Cardy boundary states. We show some interesting examples of fractional and twisted branes on orbifold spaces.

•Jan 1, 2002•7 citations
We give an explicit construction of the complete set of Cardy boundary states that respect the extended chiral algebra for symmetric product orbifolds. The states are labelled by a choice of seed theory boundary states as well as a choice of representations of the symmetric group. At large NNN, we analyze the BCFT data which is relevant for holography, namely the boundary entropy and the one-point functions of single-trace operators. In some cases, typical boundary states are compatible with a bulk description in terms of an End-of-the-World brane along with backreacted matter fields. We discuss the significance of these results for the AdS/BCFT correspondence.
States, symmetries and correlators of TTˉT\bar{T}TTˉ and $ J\bar{T} $ symmetric orbifolds
We derive various properties of symmetric product orbifolds of T\bar T T T ‾ and J\bar T J T ‾ - deformed CFTs from a field-theoretical perspective. First, we generalise the known formula for the torus partition function of a symmetric orbifold theory in terms of the one of the seed to non-conformal two-dimensional QFTs; specialising this to seed T\bar T T T ‾ and J\bar T J T ‾ - deformed CFTs reproduces previous results in the literature. Second, we show that the single-trace T\bar T T T ‾ and J\bar T J T ‾ deformations preserve the Virasoro and Kac-Moody symmetries of the undeformed symmetric product orbifold CFT, including their fractional counterparts, as well as the KdV charges. Finally, we discuss correlation functions in these theories. By extending a previously-proposed basis of operators for J\bar T J T ‾ - deformed CFTs to the single-trace case, we explicitly compute the correlation functions of both untwisted and twisted-sector operators and compare them to an appropriate set of holographic correlators. Our derivations are based mainly on Hilbert space techniques and completely avoid the use of conformal invariance, which is not present in these models.
We study the space of the allowed boundary states in a particular c=1 conformal field theory, the symmetric orbifold of the level one SU(2) WZW model, where the orbifolding group G is a generic binary finite subgroup of SU(2). We especially construct generic boundary states in the orbifold, which can be extended from the Cardy states decomposed into Virasoro Ishibashi states. Our result involves conformal boundary states parameterized by the quotient SU(2)/G, and the fractional boundary states sitting at every fixed-point in the quotient. We find also that a conformal boundary state at a fixed-point in the quotient becomes a linear combination of the fractional boundary states sitting at the fixed-point. To be complete, we check the mutual consistency among all the boundary states we construct.
Bridging boundaries: TT‾ T\overline{T} TT, double holography, and reflected entropy
A bstract We investigate the reflected entropy for bipartite mixed state configurations in a TT‾ T\overline{T} TT T T ¯ deformed boundary conformal field theory in 2 dimensions (BCFT 2 ). The bulk dual is described by asymptotically AdS 3 geometries with the cut off surface pushed deeper into the bulk and truncated by an end of the world brane. We obtain the reflected entropy up to a linear order in the radial cut-off for static and time dependent configurations involving an eternal black hole, from the island and defect extremal surface (DES) prescriptions in the context of the deformed AdS/BCFT. We observe agreement of the leading order correction for all cases between the two prescriptions. We also obtain the analogous of the Page curves for the reflected entropy and investigate the modification due to the TT‾ T\overline{T} TT T T ¯ deformation.
We present a large and universal class of new boundary states which break part of the chiral symmetry in the underlying bulk theory. Our formulas are based on coset constructions and they can be regarded as a non-abelian generalization of the ideas that were used by Maldacena, Moore and Seiberg to build new boundary states for SU(N). We apply our expressions to construct defect lines joining two conformal field theories with possibly different central charge. Such defects can occur e.g. in the AdS/CFT correspondence when branes extend to the boundary of the AdS-space.
We study the symmetry resolution of the entanglement entropy of an interval in two-dimensional conformal field theories (CFTs), by relating the bipartition to the geometry of an annulus with conformal boundary conditions. In the presence of extended symmetries such as Kac-Moody type current algebrae, symmetry resolution is possible only if the boundary conditions on the annulus preserve part of the symmetry group, i.e. if the factorization map associated with the spatial bipartition is compatible with the symmetry in question. The partition function of the boundary CFT (BCFT) is then decomposed in terms of the characters of the irreducible representations of the symmetry group preserved by the boundary conditions. We demonstrate that this decomposition already provides the symmetry resolution of the entanglement spectrum of the corresponding bipartition. Considering the various terms of the partition function associated with the same representation, or charge sector, the symmetry-resolved Rényi entropies can be derived to all orders in the UV cutoff expansion without the need to compute the charged moments. We apply this idea to the theory of a free massless boson with U(1) U ( 1 ) , \mathbb{R} ℝ and \mathbb{Z}_2 ℤ 2 symmetry.