Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2011-04-28
JHEP 1106:056,2011
Physics
High Energy Physics
High Energy Physics - Theory
36 pages, 8 figures
Scientific paper
10.1007/JHEP06(2011)056
Brane tilings, sometimes called dimer models, are a class of bipartite graphs on a torus which encode the gauge theory data of four-dimensional SCFTs dual to D3-branes probing toric Calabi--Yau threefolds. An efficient way of encoding this information exploits the theory of dessin d'enfants, expressing the structure in terms of a permutation triple, which is in turn related to a Belyi pair, namely a holomorphic map from a torus to a P^1 with three marked points. The procedure of a-maximization, in the context of isoradial embeddings of the dimer, also associates a complex structure to the torus, determined by the R-charges in the SCFT, which can be compared with the Belyi complex structure. Algorithms for the explicit construction of the Belyi pairs are described in detail. In the case of orbifolds, these algorithms are related to the construction of covers of elliptic curves, which exploits the properties of Weierstrass elliptic functions. We present a counterexample to a previous conjecture identifying the complex structure of the Belyi curve to the complex structure associated with R-charges.
Hanany Amihay
He Yang-Hui
Jejjala Vishnu
Pasukonis Jurgis
Ramgoolam Sanjaye
No associations
LandOfFree
The Beta Ansatz: A Tale of Two Complex Structures does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The Beta Ansatz: A Tale of Two Complex Structures, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Beta Ansatz: A Tale of Two Complex Structures will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-451089