A geometric recipe for twisted superpotentials

Hollands, Lotte; Rüter, Philipp; Szabo, Richard J.

doi:10.1007/jhep12(2021)164

Cited by 11 publications

(14 citation statements)

References 113 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This limit enjoys a close relation to quantum integrability [6,56,57] and many other applications (e.g. [58,59,60,61,62,63]). Thus, in the special case we have considered, our result relates different notions of quantum curve appearing in the literature.…”

Section: Rtr4mentioning

confidence: 56%

Quantum curves from refined topological recursion: the genus 0 case

Kidwai¹,

Osuga²

2022

Preprint

View full text Add to dashboard Cite

We formulate geometrically (without reference to physical models) a refined topological recursion applicable to genus zero curves of degree two, inspired by Chekhov-Eynard and Marchal, introducing new degrees of freedom in the process. For such curves, we prove the fundamental properties of the recursion analogous to the unrefined case. We show the quantization of spectral curves due to Iwaki-Koike-Takei can be generalized to this setting and give the explicit formula, which turns out to be related to the unrefined case by a simple transformation. For an important collection of examples, we write down the quantum curves and find that in the Nekrasov-Shatashvili limit, they take an especially simple form.

show abstract

Section: Rtr4mentioning

confidence: 56%

Quantum curves from refined topological recursion: the genus 0 case

Kidwai¹,

Osuga²

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Spectral networks are also known as Stokes graphs in the exact WKB analysis, where they encode the Stokes phenomena of linear differential operators d(ϵ) (also known as Schrödinger operators or more generally g-opers) on (punctured) Riemann surfaces. See for instance [63,Section 4.4] for a brief introduction and references.…”

Section: Exact Wkb For Difference Operatorsmentioning

confidence: 99%

“…In parallel developments in a different context, it was realized in [60,63] that Borel resummation plays a central role in the geometric formulation of the effective twisted superpotential W eff of a four-dimensional N = 2 theory T 4d of class S in the 1 2 Ω-background R 2 ϵ × R 2 . This was motivated by a conjecture of Nekrasov, Rosly and Shatashvili [87], which says that the superpotential W eff may be obtained as a generating function of opers in terms of a special kind of Darboux coordinates on the associated moduli space of complexified flat connections.…”

Section: Introductionmentioning

confidence: 99%

“…It was proposed in [62,63] that the generalized superpotential W eff ϑ ′ has a natural physical interpretation in terms of the 4d N = 2 theory T . It was argued that each Stokes sector corresponds to a certain IR boundary condition of the 4d theory T in the 1 2 Ω-background R 2 ϵ × R 2 labeled by ϑ ′ , which can be explicitly described by coupling a 3d N = 2 theory of class R to the boundary S 1 × R 2 of the 1 2 Ω-background.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Quantum Curves, Resurgence and Exact WKB

Alim¹,

Hollands²,

Tulli³

2023

SIGMA

View full text Add to dashboard Cite

We study the non-perturbative quantum geometry of the open and closed topological string on the resolved conifold and its mirror. Our tools are finite difference equations in the open and closed string moduli and the resurgence analysis of their formal power series solutions. In the closed setting, we derive new finite difference equations for the refined partition function as well as its Nekrasov-Shatashvili (NS) limit. We write down a distinguished analytic solution for the refined difference equation that reproduces the expected non-perturbative content of the refined topological string. We compare this solution to the Borel analysis of the free energy in the NS limit. We find that the singularities of the Borel transform lie on infinitely many rays in the Borel plane and that the Stokes jumps across these rays encode the associated Donaldson-Thomas invariants of the underlying Calabi-Yau geometry. In the open setting, the finite difference equation corresponds to a canonical quantization of the mirror curve. We analyze this difference equation using Borel analysis and exact WKB techniques and identify the 5d BPS states in the corresponding exponential spectral networks. We furthermore relate the resurgence analysis in the open and closed setting. This guides us to a five-dimensional extension of the Nekrasov-Rosly-Shatashvili proposal, in which the NS free energy is computed as a generating function of q-difference opers in terms of a special set of spectral coordinates. Finally, we examine two spectral problems describing the corresponding quantum integrable system.

show abstract

“…The separating and finite curves are also called Stokes curves in direction ϑ, and they form the Stokes graph in direction ϑ with vertices at the branch points on C. The Stokes graph is also called a WKB spectral network, while its oriented edges (the Stokes curves) are also called S-walls and double walls for separating and finite curves, respectively (see [HRS21] for an up to date review); we will use both nomenclatures interchangeably in this paper.…”

Section: Ideal Triangulationsmentioning

confidence: 99%

Novel wall-crossing behaviour in rank one $\mathcal{N}=2^*$ gauge theory

Rüter,

Szabo

2021

Preprint

Self Cite

View full text Add to dashboard Cite

We study the BPS spectrum of four-dimensional N = 2 supersymmetric Yang-Mills theory with gauge group SU(2) and a massive adjoint hypermultiplet, which has an extremely intricate structure with infinite spectrum in all chambers of its Coulomb moduli space, and is not well understood. We build on previous results by employing the BPS quiver description of the spectrum, and explore the qualitative features in detail using numerical techniques. We find novel and unexpected behaviour in the form of wall-crossings involving interactions between BPS particles with negative electric-magnetic pairings, which we interpret in terms of the reverse orderings of the usual wall-crossing formulas for rank one N = 2 field theories. This identifies new a priori unrelated states in the spectrum.

show abstract

A geometric recipe for twisted superpotentials

Cited by 11 publications

References 113 publications

Quantum curves from refined topological recursion: the genus 0 case

Quantum curves from refined topological recursion: the genus 0 case

Quantum Curves, Resurgence and Exact WKB

Novel wall-crossing behaviour in rank one $\mathcal{N}=2^*$ gauge theory

Contact Info

Product

Resources

About