# BPS States, Torus Links and Wild Character Varieties

@article{Diaconescu2017BPSST, title={BPS States, Torus Links and Wild Character Varieties}, author={Duiliu-Emanuel Diaconescu and Ron Y. Donagi and Tony Pantev}, journal={Communications in Mathematical Physics}, year={2017}, volume={359}, pages={1027-1078} }

A string theoretic framework is constructed relating the cohomology of wild character varieties to refined stable pair theory and torus link invariants. Explicit conjectural formulas are derived for wild character varieties with a unique irregular point on the projective line. For this case, this leads to a conjectural colored generalization of existing results of Hausel, Mereb and Wong as well as Shende, Treumann and Zaslow.

## 11 Citations

### Twisted spectral correspondence and torus knots

- MathematicsJournal of Knot Theory and Its Ramifications
- 2020

Cohomological invariants of twisted wild character varieties as constructed by Boalch and Yamakawa are derived from enumerative Calabi–Yau geometry and refined Chern–Simons invariants of torus knots.…

### Local curves, wild character varieties, and degenerations

- Mathematics
- 2017

Conjectural results for cohomological invariants of wild character varieties are obtained by counting curves in degenerate Calabi-Yau threefolds. A conjectural formula for E-polynomials is derived…

### Intersection cohomology of character varieties for punctured Riemann surfaces

- Mathematics
- 2022

We study intersection cohomology of character varieties for punctured Riemann surfaces with prescribed monodromies around the punctures. Relying on previous result from Mellit [Mel17b] for semisimple…

### Refined large N duality for torus knots

- Mathematics
- 2017

We formulate large N duality of U(N) refined Chern-Simons theory with a torus
knot/link in S^3. By studying refined BPS states in M-theory, we provide the explicit form of
low-energy effective…

### Motivic classes of moduli of Higgs bundles and moduli of bundles with connections

- Mathematics
- 2017

Let X be a smooth projective curve over a field of characteristic zero. We calculate the motivic class of the moduli stack of semistable Higgs bundles on X. We also calculate the motivic class of the…

### Topological strings, quiver varieties, and Rogers–Ramanujan identities

- Mathematics
- 2017

Motivated by some recent works on BPS invariants of open strings/knot invariants, we guess there may be a general correspondence between the Ooguri–Vafa invariants of toric Calabi–Yau 3-folds and…

### Deletion-contraction triangles for Hausel-Proudfoot varieties

- Mathematics
- 2019

To a graph, Hausel and Proudfoot associate two complex manifolds, B and D, which behave, respectively like moduli of local systems on a Riemann surface, and moduli of Higgs bundles. For instance, B…

### Refined large N duality for knots

- Mathematics
- 2017

We formulate large $N$ duality of $\mathrm{U}(N)$ refined Chern-Simons theory with a torus knot/link in $S^3$. By studying refined BPS states in M-theory, we provide the explicit form of low-energy…

### Spectral Data For L^2 Cohomology

- Mathematics
- 2018

SPECTRAL DATA FOR L COHOMOLOGY Xiaofei Jin Tony Pantev We study the spectral data for the higher direct images of a parabolic Higgs bundle along a map between a surface and a curve with both vertical…

### Blowup equations for refined topological strings

- MathematicsJournal of High Energy Physics
- 2018

A bstractGöttsche-Nakajima-Yoshioka K-theoretic blowup equations characterize the Nekrasov partition function of five dimensional N=1$$ \mathcal{N}=1 $$ supersymmetric gauge theories compactified on…

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