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.

show abstract

“…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.

673

1,584

View full text Add to dashboard Cite

show abstract

“…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.

View full text Add to dashboard Cite

show abstract

“…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

View full text Add to dashboard Cite

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.

show abstract

Fusion rules and modular transformations in 2D conformal field theory

Cited by 1,293 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

Contact Info

Product

Resources

About