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.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, 20030 citations

Boundary Structure and Module Decomposition of the Bosonic $Z_2$ Orbifold Models with $R^2=1/2k$ 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.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, 20020 citations

Twisted boundary states in c=1 coset theories

Hiroshi Ishikawa, Atsushi Yamaguchi

素粒子論研究Dec 20, 20020 citations

Boundary Structure and Module Decomposition of the Bosonic

Z_2

Orbifold Models with

R^2=1/2k

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.