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

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

Atsushi Yamaguchi

Published Sep 10, 2003• 0 citations
OpenAlex

Abstract

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.

Related papers

Conformal Boundary States in

Atsushi Yamaguchi

We construct boundary states in a particular c = 1 conformal field theory, the orbifold with G a binary finite subgroup of SU(2). These states preserve the conformal symmetry, at least, but break rational symmetries of the orbifold in general.

arXiv:hep-th/0309102•Progress of Theoretical Physics•Jul 1, 2004•2 citations

Symmetry-breaking boundary states for WZW models

Daniel Blakeley, A. Recknagel

Starting with the SU ( 2 ) k WZW model, we construct boundary states that generically preserve only a parafermion times Virasoro subalgebra of the full affine Lie algebra symmetry of the bulk model. The boundary states come in families: intervals for generic k , quotients of SU ( 2 ) by discrete groups if k is a square. In that case, special members of the families can be viewed as superpositions of rotated Cardy branes. Using embeddings of SU ( 2 ) into higher groups, the new boundary states can be lifted to symmetry-breaking branes for other WZW models.

arXiv:0705.1068•Nuclear Physics B•Aug 7, 2008•7 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

Boundary Structure and Module Decomposition of the Bosonic $Z_2$ Orbifold Models with $R^2=1/2k$

Hatzinikitas, A, Smyrnakis, J M

The $Z_2$ bosonic orbifold models with compactification radius $R^2=1/2k$ are examined in the presence of boundaries. Demanding the extended algebra characters to have definite conformal dimension and to consist of an integer sum of Virasoro characters, we arrive at the right splitting of the partition function. This is used to derive a free field representation of a complete, consistent set of boundary states, without resorting to a basis of the extended algebra Ishibashi states. Finally the modules of the extended symmetry algebra that correspond to the finitely many characters are identified inside the direct sum of Fock modules that constitute the space of states of the theory.

•Mar 14, 2002•0 citations

arXiv : The Spectrum of Boundary States in Symmetric Orbifolds

Alexandre Belin, James Sully, Shovon Biswas

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.

•Oct 11, 2021•0 citations

From orbifolding conformal field theories to gauging topological phases

Xiao Chen, Abhishek Roy, Jeffrey C. Y. Teo +1 more

Topological phases of matter in (2+1) dimensions are commonly equipped with global symmetries, such as electric-magnetic duality in gauge theories and bilayer symmetry in fractional quantum Hall states. Gauging these symmetries into local dynamical ones is one way of obtaining exotic phases from conventional systems. We study this using the bulk-boundary correspondence and applying the orbifold construction to the (1+1)-dimensional edge described by a conformal field theory (CFT). Our procedure puts twisted boundary conditions into the partition function and predicts the fusion, spin, and braiding behavior of anyonic excitations after gauging. We demonstrate this for the electric-magnetic self-dual ${\mathbb{Z}}_{N}$ gauge theory, the twofold symmetric $\text{SU}{(3)}_{1}$, and the ${S}_{3}$-symmetric $\text{SO}{(8)}_{1}$ Wess-Zumino-Witten theories.

arXiv:1706.00557•Physical review. B./Physical review. B•Sep 27, 2017•14 citations
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.
Starting with the SU ( 2 ) k WZW model, we construct boundary states that generically preserve only a parafermion times Virasoro subalgebra of the full affine Lie algebra symmetry of the bulk model. The boundary states come in families: intervals for generic k , quotients of SU ( 2 ) by discrete groups if k is a square. In that case, special members of the families can be viewed as superpositions of rotated Cardy branes. Using embeddings of SU ( 2 ) into higher groups, the new boundary states can be lifted to symmetry-breaking branes for other WZW models.
Boundary Structure and Module Decomposition of the Bosonic Z2Z_2Z2​ Orbifold Models with R2=1/2kR^2=1/2kR2=1/2k
The Z2Z_2Z2​ bosonic orbifold models with compactification radius R2=1/2kR^2=1/2kR2=1/2k are examined in the presence of boundaries. Demanding the extended algebra characters to have definite conformal dimension and to consist of an integer sum of Virasoro characters, we arrive at the right splitting of the partition function. This is used to derive a free field representation of a complete, consistent set of boundary states, without resorting to a basis of the extended algebra Ishibashi states. Finally the modules of the extended symmetry algebra that correspond to the finitely many characters are identified inside the direct sum of Fock modules that constitute the space of states of the theory.
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.
Topological phases of matter in (2+1) dimensions are commonly equipped with global symmetries, such as electric-magnetic duality in gauge theories and bilayer symmetry in fractional quantum Hall states. Gauging these symmetries into local dynamical ones is one way of obtaining exotic phases from conventional systems. We study this using the bulk-boundary correspondence and applying the orbifold construction to the (1+1)-dimensional edge described by a conformal field theory (CFT). Our procedure puts twisted boundary conditions into the partition function and predicts the fusion, spin, and braiding behavior of anyonic excitations after gauging. We demonstrate this for the electric-magnetic self-dual ZN{\mathbb{Z}}_{N}ZN​ gauge theory, the twofold symmetric SU(3)1\text{SU}{(3)}_{1}SU(3)1​, and the S3{S}_{3}S3​-symmetric SO(8)1\text{SO}{(8)}_{1}SO(8)1​ Wess-Zumino-Witten theories.