Supersymmetric Ground States of 3d $\mathcal{N}=4$ Gauge Theories on a  Riemann Surface

Bullimore, Mathew; Ferrari, Andrea E. V.; Kim, Heeyeon

doi:10.21468/scipostphys.12.2.072

Cited by 11 publications

(27 citation statements)

References 39 publications

(65 reference statements)

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“…There is also closely related work in 3d N = 4 theories such as [50,51]. We do not develop this point of view much in the current paper; however, it seems likely that in future developments this will be an important perspective.…”

Section: Introductionmentioning

confidence: 92%

Exponential Networks, WKB and the Topological String

Grassi¹,

Hao²,

Neitzke³

2022

Preprint

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We propose a connection between 3d-5d exponential networks and exact WKB for difference equations associated to five dimensional Seiberg-Witten curves, or equivalently, to quantum mirror curves to toric Calabi-Yau threefolds X: the singularities in the Borel planes of local solutions to such difference equations correspond to central charges of 3d-5d BPS KK-modes, and the central charges of 5d BPS KK-modes are related to the singularities in the Borel planes of the closed topological string free energy on X. It follows that there should be distinguished local solutions of the difference equation in each domain of the complement of the exponential network, and these solutions jump at the walls of the network. We verify this picture in detail in two simple examples of 3d-5d systems, corresponding to taking the toric Calabi-Yau X to be either C 3 or the resolved conifold. We provide the full list of local solutions in each sector of the Borel plane and in each domain of the complement of the exponential network, and find that local solutions in disconnected domains correspond to non-perturbative open topological string amplitudes on X with insertions of branes at different positions of the toric diagram. We also study the Borel summation of the closed refined topological string free energy on X and the corresponding non-perturbative effects.

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Section: Introductionmentioning

confidence: 92%

Exponential Networks, WKB and the Topological String

Grassi¹,

Hao²,

Neitzke³

2022

Preprint

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“…More generally, QFT techniques developed in [50,[176][177][178] predict that the genus-g state space…”

Section: The Category Of Line Operators Cmentioning

confidence: 99%

“…The state space on a genus-g surface Σ g may be computed by reducing the B-twisted theory on Σ g × R t to a 1d B-twisted quantum mechanics on R t . This can be done very explicitly starting from the twisted BV action (2.6), and was also described some time ago in [37,71] (or see the recent [176,177]).…”

Section: State Spaces and Indices For T B Hypermentioning

confidence: 99%

“…An alternative quantization is pursued in [177]. There, a real mass 'm R ' for a maximal torus U (1) m ⊂ SU (2) m is introduced, related to deforming by a complexified connection along the 'time' direction.…”

Section: State Spaces and Indices For T B Hypermentioning

confidence: 99%

“…A geometric-quantization-like approach for constructing state spaces of general 3d N = 2 theories in the HT twist was developed in [176], and extended to twists of 3d N = 4 theories in [177]. Some abstract properties of state spaces in the topological twists of 3d N = 4 theories were derived in [50].…”

Section: Full State Spacesmentioning

confidence: 99%

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A QFT for non-semisimple TQFT

Creutzig¹,

Dimofte²,

Garner³

et al. 2021

Preprint

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We construct a family of 3d quantum field theories T A n,k that conjecturally provide a physical realization -and derived generalization -of non-semisimple mathematical TQFT's based on the modules for the quantum group U q (sl n ) at an even root of unity q = exp(iπ/k). The theories T A n,k are defined as topological twists of certain 3d N = 4 Chern-Simons-matter theories, which also admit string/M-theory realizations. They may be thought of as SU (n) k−n Chern-Simons theories, coupled to a twisted N = 4 matter sector (the source of non-semisimplicity). We show that T A n,k admits holomorphic boundary conditions supporting two different logarithmic vertex operator algebras, one of which is an sl n -type Feigin-Tipunin algebra; and we conjecture that these two vertex operator algebras are related by a novel logarithmic level-rank duality. (We perform detailed computations to support the conjecture.) We thus relate the category of line operators in T A n,k to the derived category of modules for a boundary Feigin-Tipunin algebra, and -using a logarithmic Kazhdan-Lusztiglike correspondence that has been established for n = 2 and expected for general n -to the derived category of U q (sl n ) modules. We analyze many other key features of T A n,k and match them from quantum-group and VOA perspectives, including deformations by flat P GL(n, C) connections, one-form symmetries, and indices of (derived) genus-g state spaces.

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BPS states meet generalized cohomology

Galakhov

2023

J. High Energ. Phys.

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In this note we review a construction of a BPS Hilbert space in an effective supersymmetric quiver theory with 4 supercharges. We argue abstractly that this space contains elements of an equivariant generalized cohomology theory $$ {E}_G^{\ast}\left(-\right) $$ E G ∗ − of the quiver representation moduli space giving concretely Dolbeault cohomology, K-theory or elliptic cohomology depending on the spacial slice is compactified to a point, a circle or a torus respectively, and something more amorphous in other cases. Furthermore BPS instantons — basic contributors to interface defects or a Berry connection — induce a BPS algebra on the BPS Hilbert spaces representing Fourier-Mukai transforms on the quiver representation moduli spaces descending to an algebra over $$ {E}_G^{\ast}\left(-\right) $$ E G ∗ − as its representation. In the cases when the quiver describes a toric Calabi-Yau three-fold (CY3) the algebra is a respective generalization of the quiver BPS Yangian algebra discussed in the literature, in more general cases it is given by an abstract generalized cohomological Hall algebra.

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Supersymmetric Ground States of 3d $\mathcal{N}=4$ Gauge Theories on a Riemann Surface

Cited by 11 publications

References 39 publications

Exponential Networks, WKB and the Topological String

Exponential Networks, WKB and the Topological String

A QFT for non-semisimple TQFT

BPS states meet generalized cohomology

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