### Abstract

Deformations of topological open string theories are described, with an emphasis on their algebraic structure. They are encoded in the mixed bulk-boundary correlators. They constitute the Hochschild complex of the open string algebra the complex of multilinear maps on the boundary Hubert space. This complex is known to have the structure of a Gerstenhaber algebra (Deligne theorem), which is also found in closed string theory. Generalising the case of function algebras with a B-field, we identify the algebraic operations of the bulk sector, in terms of the mixed correlators. This gives a physical realisation of the Deligne theorem. We translate to the language of certain operads (spaces of d-discs with gluing) and d-algebras, and comment on generalisations, notably to the AdS/CFT correspondence. The formalism is applied to the topological A- and B-models on the disc.

Original language | English (US) |
---|---|

Journal | Journal of High Energy Physics |

Volume | 5 |

Issue number | 1 |

State | Published - 2001 |

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### Keywords

- Chern-Simons Theories
- Conformal Field Models in String Theory
- Topological Field Theories

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Journal of High Energy Physics*,

*5*(1).

**Deformations of topological open strings.** / Hofman, Christiaan; Ma, Whee Ky.

Research output: Contribution to journal › Article

*Journal of High Energy Physics*, vol. 5, no. 1.

}

TY - JOUR

T1 - Deformations of topological open strings

AU - Hofman, Christiaan

AU - Ma, Whee Ky

PY - 2001

Y1 - 2001

N2 - Deformations of topological open string theories are described, with an emphasis on their algebraic structure. They are encoded in the mixed bulk-boundary correlators. They constitute the Hochschild complex of the open string algebra the complex of multilinear maps on the boundary Hubert space. This complex is known to have the structure of a Gerstenhaber algebra (Deligne theorem), which is also found in closed string theory. Generalising the case of function algebras with a B-field, we identify the algebraic operations of the bulk sector, in terms of the mixed correlators. This gives a physical realisation of the Deligne theorem. We translate to the language of certain operads (spaces of d-discs with gluing) and d-algebras, and comment on generalisations, notably to the AdS/CFT correspondence. The formalism is applied to the topological A- and B-models on the disc.

AB - Deformations of topological open string theories are described, with an emphasis on their algebraic structure. They are encoded in the mixed bulk-boundary correlators. They constitute the Hochschild complex of the open string algebra the complex of multilinear maps on the boundary Hubert space. This complex is known to have the structure of a Gerstenhaber algebra (Deligne theorem), which is also found in closed string theory. Generalising the case of function algebras with a B-field, we identify the algebraic operations of the bulk sector, in terms of the mixed correlators. This gives a physical realisation of the Deligne theorem. We translate to the language of certain operads (spaces of d-discs with gluing) and d-algebras, and comment on generalisations, notably to the AdS/CFT correspondence. The formalism is applied to the topological A- and B-models on the disc.

KW - Chern-Simons Theories

KW - Conformal Field Models in String Theory

KW - Topological Field Theories

UR - http://www.scopus.com/inward/record.url?scp=33744871747&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33744871747&partnerID=8YFLogxK

M3 - Article

VL - 5

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 1

ER -