Abelian conformal field theory and determinant bundles

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

Resumé

Following [10], we study a so-called bc-ghost system of zero conformal dimension from the viewpoint of [14, 16]. We show that the ghost vacua construction results in holomorphic line bundles with connections over holomorphic families of curves. We prove that the curvature of these connections are up to a scale the same as the curvature of the connections constructed in [14, 16]. We study the sewing construction for nodal curves and its explicit relation to the constructed connections. Finally we construct preferred holomorphic sections of these line bundles and analyze their behaviour near nodal curves. These results are used in [4] to construct modular functors form the conformal field theories given in [14, 16] by twisting with an appropriate factional power of this Abelian theory.
OriginalsprogEngelsk
TidsskriftInternational Journal of Mathematics
Vol/bind18
Udgave nummer8
Sider (fra-til)919-993
Antal sider75
ISSN0129-167X
DOI
StatusUdgivet - 2007
Udgivet eksterntJa

Fingeraftryk

Conformal Field Theory
Nodal Curve
Bundle
Determinant
Line Bundle
Curvature
Functor
Curve
Zero

Citer dette

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abstract = "Following [10], we study a so-called bc-ghost system of zero conformal dimension from the viewpoint of [14, 16]. We show that the ghost vacua construction results in holomorphic line bundles with connections over holomorphic families of curves. We prove that the curvature of these connections are up to a scale the same as the curvature of the connections constructed in [14, 16]. We study the sewing construction for nodal curves and its explicit relation to the constructed connections. Finally we construct preferred holomorphic sections of these line bundles and analyze their behaviour near nodal curves. These results are used in [4] to construct modular functors form the conformal field theories given in [14, 16] by twisting with an appropriate factional power of this Abelian theory.",
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Abelian conformal field theory and determinant bundles. / Andersen, Jørgen Ellegaard; Ueno, K.

I: International Journal of Mathematics, Bind 18, Nr. 8, 2007, s. 919-993.

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

TY - JOUR

T1 - Abelian conformal field theory and determinant bundles

AU - Andersen, Jørgen Ellegaard

AU - Ueno, K.

PY - 2007

Y1 - 2007

N2 - Following [10], we study a so-called bc-ghost system of zero conformal dimension from the viewpoint of [14, 16]. We show that the ghost vacua construction results in holomorphic line bundles with connections over holomorphic families of curves. We prove that the curvature of these connections are up to a scale the same as the curvature of the connections constructed in [14, 16]. We study the sewing construction for nodal curves and its explicit relation to the constructed connections. Finally we construct preferred holomorphic sections of these line bundles and analyze their behaviour near nodal curves. These results are used in [4] to construct modular functors form the conformal field theories given in [14, 16] by twisting with an appropriate factional power of this Abelian theory.

AB - Following [10], we study a so-called bc-ghost system of zero conformal dimension from the viewpoint of [14, 16]. We show that the ghost vacua construction results in holomorphic line bundles with connections over holomorphic families of curves. We prove that the curvature of these connections are up to a scale the same as the curvature of the connections constructed in [14, 16]. We study the sewing construction for nodal curves and its explicit relation to the constructed connections. Finally we construct preferred holomorphic sections of these line bundles and analyze their behaviour near nodal curves. These results are used in [4] to construct modular functors form the conformal field theories given in [14, 16] by twisting with an appropriate factional power of this Abelian theory.

U2 - 10.1142/S0129167X07004369

DO - 10.1142/S0129167X07004369

M3 - Journal article

VL - 18

SP - 919

EP - 993

JO - International Journal of Mathematics

JF - International Journal of Mathematics

SN - 0129-167X

IS - 8

ER -