# 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…

## 2 Citations

### Combinatoric topological string theories and group theory algorithms

- Mathematics
- 2022

A number of ﬁnite algorithms for constructing representation theoretic data from group multiplications in a ﬁnite group G have recently been shown to be related to amplitudes for combinatoric…

### Comments on summing over bordisms in TQFT

- PhysicsJournal of High Energy Physics
- 2022

Recent works in quantum gravity, motivated by the “factorization problem” and “baby universes,” have considered sums over bordisms with fixed boundaries in topological quantum field theory (TQFT). We…

## References

SHOWING 1-10 OF 84 REFERENCES

### BPS states, conserved charges and centres of symmetric group algebras

- MathematicsJournal of High Energy Physics
- 2020

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

- Mathematics
- 2011

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

- PhysicsJournal of High Energy Physics
- 2021

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

- Mathematics
- 2011

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

- Mathematics
- 2019

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

- Mathematics
- 2020

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

- Mathematics
- 2020

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

- Mathematics
- 2015

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

- Mathematics
- 2010

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…