Integrality, duality and finiteness in combinatoric topological strings

@article{Koch2022IntegralityDA,
  title={Integrality, duality and finiteness in combinatoric topological strings},
  author={Robert De Mello Koch and Yang-Hui He and Garreth James Kemp and Sanjaye Ramgoolam},
  journal={Journal of High Energy Physics},
  year={2022}
}
Abstract A remarkable result at the intersection of number theory and group theory states that the order of a finite group G (denoted |G|) is divisible by the dimension dR of any irreducible complex representation of G. We show that the integer ratios $$ {\left|G\right|}^2/{d}_R^2 $$ G 2 / d R 2 are combinatorially constructible using finite algorithms which take as input the amplitudes of combinatoric topological strings (G-CTST) of finite groups based on 2D Dijkgraaf… 
Combinatoric topological string theories and group theory algorithms
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References

SHOWING 1-10 OF 83 REFERENCES
On effective theories of topological strings
BPS states, conserved charges and centres of symmetric group algebras
In N $$ \mathcal{N} $$ = 4 SYM with U( N ) gauge symmetry, the multiplicity of half-BPS states with fixed dimension can be labelled by Young diagrams and can be distinguished using conserved charges
Toric CFTs, permutation triples, and Belyi pairs
Four-dimensional CFTs dual to branes transverse to toric Calabi-Yau threefolds have been described by bipartite graphs on a torus (dimer models). We use the theory of dessins d’enfants to describe
2d TQFTs and baby universes
Abstract In this work, we extend the 2d topological gravity model of [1] to have as its bulk action any open/closed TQFT obeying Atiyah’s axioms. The holographic duals of these topological gravity
The beta ansatz: a tale of two complex structures
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
JT gravity as a matrix integral
We present exact results for partition functions of Jackiw-Teitelboim (JT) gravity on two-dimensional surfaces of arbitrary genus with an arbitrary number of boundaries. The boundaries are of the
Quantum mechanics of bipartite ribbon graphs: Integrality, Lattices and Kronecker coefficients
We define solvable quantum mechanical systems on a Hilbert space spanned by bipartite ribbon graphs with a fixed number of edges. The Hilbert space is also an associative algebra, where the product
Quarter-BPS states, multi-symmetric functions and set partitions
We give a construction of general holomorphic quarter BPS operators in $ \mathcal{N}=4$ SYM at weak coupling with $U(N)$ gauge group at finite $N$. The construction employs the Mobius inversion
Multi-Matrix Models and Noncommutative Frobenius Algebras Obtained from Symmetric Groups and Brauer Algebras
It has been understood that correlation functions of multi-trace operators in $${\mathcal{N}=4}$$N=4 SYM can be neatly computed using the group algebra of symmetric groups or walled Brauer algebras.
From Matrix Models and quantum fields to Hurwitz space and the absolute Galois group
We show that correlators of the hermitian one-Matrix model with a general potential can be mapped to the counting of certain triples of permutations and hence to counting of holomorphic maps from
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