Quantum K theory of symplectic Grassmannians

Gu, W.; Mihalcea, L.; Sharpe, E.; Zou, H.

doi:10.48550/arxiv.2008.04909

Cited by 7 publications

(12 citation statements)

References 36 publications

(65 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Besides the charged-p projective space moduli, we have an extra label due to the Wilson loop e 2iπRσ 2 [37,38]. Furthermore, one can show that e l * 2iπRσ 2 is a representation of the Z p one-form symmetry with the charge l mod p [1,37].…”

Section: D N = 2 Chern-simons Matter Theoriesmentioning

confidence: 88%

Vacuum Structures Revisited

2021

Preprint

View full text Add to dashboard Cite

We consider the relationship between the higher symmetry and the dynamical decomposition in supersymmetric gauge theory in various dimensions by studying the semi-classical potential energy. We observe that besides the scalar moduli we shall also include the field strength F 0•••d in the vacuum moduli in the 1+d dimensional theory with a Z p d-form symmetry. In gauge theory for charge-p matters with this symmetry, we find that the vacua decompose into p different universes at an intermediate scale, which means no dynamical domain wall can interpolate between them. In our setup, we re-derive the existing results on the decomposition in various dimensions. In four dimensions, we propose a UV gauge theory for the generalized super Yang-Mills theory, whose instanton sectors are restricted to the topological number with integer multiples of p.

show abstract

Section: D N = 2 Chern-simons Matter Theoriesmentioning

confidence: 88%

Vacuum Structures Revisited

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…The term N c arises from integrating out the extra N = 2 chiral multiplet needed to build the N = 4 vector multiplet, and the −N f /2 from integrating out half of the N = 4 hypermultiplets. More details about how to get the quantum K-theory from formula (2.12) with these levels (2.13) can be found in [17,32]. One may notice that the levels (2.13) corresponding to Givental-Lee's quantum K-theory of a Grassmannian are different from those proposed by Kapustin and Willett.…”

Section: (212)mentioning

confidence: 95%

“…Notice that we can divide the Chern-Simons level k U (Nc) into k U (1) and k SU (Nc) . Following [17], we write the twisted effective superpotential as…”

Section: Dmentioning

confidence: 99%

“…This can also happen in non-abelian GLSMs, which has been used in [16,17] for computing the quantum cohomology and K-theory of the Lagrangian Grassmannian. Thus, for a GLSM on R 2 × S 1 , an extension of Witten's analysis still holds.…”

Section: A Simple Extension Of Witten's Correspondencementioning

confidence: 99%

“…This idea was used in [16,17] to compute the quantum cohomology of Lagrangian Grassmannians, matching the results obtained from a different approach in the mathematical literature. And if one can lift the two-dimensional effective theory to a 3d theory on R 2 × S 1 with the effective theory (1.4), one could then obtain the quantum K-theory of Lagrangian Grassmannians, which would produce new mathematical results.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On Phases of 3d ${\cal N}=2$ Chern-Simons-Matter Theories

Gu,

Pei,

Zhang

2021

Preprint

View full text Add to dashboard Cite

We investigate phases of 3d N = 2 Chern-Simons-matter theories, extending to three dimensions the celebrated correspondence between 2d gauged Wess-Zumino-Witten (GWZW) models and non-linear sigma models (NLSMs) with geometric targets. We find that although the correspondence in 3d and 2d are closely related by circle compactification, an important subtlety arises in this process, changing the phase structure of the 3d theory. Namely, the effective theory obtained from the circle compactification of a phase of a 3d N = 2 gauge theory is, in general, different from the phase of the 3d N = 2 theory on R 2 × S 1 , which means taking phases of a 3d gauge theory do not necessary commute with compactification. We compute the Witten index of each effective theory to check this observation. Furthermore, when the matter fields have the same non-minimal charges, the 3d N = 2 Chern-Simons-matter theory with a proper Chern-Simons level will decompose into several identical 2d gauged linear sigma models (GLSMs) for the same target upon reduction to 2d. To illustrate this phenomenon, we investigate how vacua of the 3d gauge theory for a weighted projective space W P [l,••• ,l] move on the field space when we change the radius of S 1 .

show abstract

BPS indices, modularity and perturbations in quantum K-theory

Jockers

Mayr²,

Ninad³

et al. 2022

J. High Energ. Phys.

View full text Add to dashboard Cite

We study a perturbation family of $$ \mathcal{N} $$ N = 2 3d gauge theories and its relation to quantum K-theory. A 3d version of the Intriligator-Vafa formula is given for the quantum K-theory ring of Grassmannians. The 3d BPS half-index of the gauge theory is connected to the theory of bilateral hypergeometric q-series, and to modular q-characters of a class of conformal field theories in a certain massless limit. Turning on 3d Wilson lines at torsion points leads to mock modular behavior. Perturbed correlators in the IR regime are computed by determining the UV-IR map in the presence of deformations.

show abstract

Quantum K theory of symplectic Grassmannians

Cited by 7 publications

References 36 publications

Vacuum Structures Revisited

Vacuum Structures Revisited

On Phases of 3d ${\cal N}=2$ Chern-Simons-Matter Theories

BPS indices, modularity and perturbations in quantum K-theory

Contact Info

Product

Resources

About