Fusion rules and modular transformations in 2D conformal field theory

We construct a cubic field theory which provides all genus amplitudes of the topological A-model for all non-compact toric Calabi-Yau threefolds. The topology of a given Feynman diagram encodes the topology of a fixed Calabi-Yau, with Schwinger parameters playing the role of Kähler classes of the threefold. We interpret this result as an operatorial computation of the amplitudes in the B-model mirror which is the quantum KodairaSpencer theory. The only degree of freedom of this theory is an unconventional chiral scalar on a Riemann surface. In this setup we identify the B-branes on the mirror Riemann surface as fermions related to the chiral boson by bosonization.

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“…On the other hand, it is well known [36,18]. Using this, we arrive at the following expression for (6.1):…”

Section: Consider Then Tmentioning

confidence: 99%

The Topological Vertex

Aganagic

Klemm

Mariño

et al. 2004

Commun. Math. Phys.

671

1,584

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“…By the Verlinde formula [22], these matrices also describe the modular transformation behavior of chiral partition functions ("characters"). By [1], the matrix Z given by (3.7) is a modular invariant (it commutes with S and T ), hence the partition function of the 2D CFT B 2D on H 2D is invariant under modular transformations.…”

Section: Haag Duality and Modular Invariancementioning

confidence: 99%

How to Remove the Boundary in CFT – An Operator Algebraic Procedure

Longo

Rehren

2008

Commun. Math. Phys.

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“…For the bulk G/G theory and a n = χ λn , expression (6.5) evaluates to an integer N (λn) (g), the Verlinde dimension of the space of conformal blocks on Σ with insertions of the primary fields with labels λ n . Explicitly [32],…”

Section: Figmentioning

confidence: 99%

Boundary WZW, G / H, G / G and CS theories

Gawędzki¹

2002

Ann. Henri Poincaré

144

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We extend the analysis [18] of the canonical structure of the Wess-Zumino-Witten theory to the bulk and boundary coset G/H models. The phase spaces of the coset theories in the closed and in the open geometry appear to coincide with those of a double ChernSimons theory on two different 3-manifolds. In particular, we obtain an explicit description of the canonical structure of the boundary G/G coset theory. The latter may be easily quantized leading to an example of a two-dimensional topological boundary field theory.

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Fusion rules and modular transformations in 2D conformal field theory

Cited by 1,270 publications

References 18 publications

The Topological Vertex

The Topological Vertex

How to Remove the Boundary in CFT – An Operator Algebraic Procedure

Boundary WZW, G / H, G / G and CS theories

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