# On Higgs branch localization of Seiberg–Witten theories on an ellipsoid

@article{Chen2015OnHB, title={On Higgs branch localization of Seiberg–Witten theories on an ellipsoid}, author={Heng-Yu Chen and Tsung-Hsuan Tsai}, journal={Progress of Theoretical and Experimental Physics}, year={2015}, volume={2016} }

In this note, we consider so-called "Higgs Branch Localization" for four dimensional N=2 field theories on 4d ellipsoid. We find a new set of saddle point equations arising from additional Higgs branch deformation term, whose solutions include both Higgs branch and BPS instanton-vortex mixed configurations. By evaluating the contour integral, we also demonstrate the ellipsoid partition almost factorizes into purely b and 1/b dependent parts, using SQCD as an explicit example. We identify…

## 31 Citations

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## References

SHOWING 1-10 OF 33 REFERENCES

### Higgs branch localization in three dimensions

- Physics
- 2014

A bstractWe show that the supersymmetric partition function of three-dimensional $ \mathcal{N} $ =2 R-symmetric Chern-Simons-matter theories on the squashed S3 and on S2× S1 can be computed with the…

### Ellipsoid partition function from Seiberg-Witten monopoles

- Mathematics
- 2015

A bstractWe study Higgs branch localization of N=2$$ \mathcal{N}=2 $$ supersymmetric theories placed on compact Euclidean manifolds. We analyze the resulting localization equations in detail on the…

### Higgs branch localization of 3d = 2 theories

- Physics, Mathematics
- 2014

We study N = 2 supersymmetric gauge theories on squashed 3-sphere and S 1 ×S 2 . Recent studies have shown that the partition functions in a class of N = 2 theories have factorized forms in terms of…

### Exact results in D = 2 supersymmetric gauge theories

- Physics
- 2013

A bstractWe compute exactly the partition function of two dimensional $ \mathcal{N} $ = (2, 2) gauge theories on S2 and show that it admits two dual descriptions: either as an integral over the…

### A new 2d/4d duality via integrability

- Mathematics
- 2011

We prove a duality, recently conjectured in arXiv:1103.5726, which relates the F-terms of supersymmetric gauge theories defined in two and four dimensions respectively. The proof proceeds by a saddle…

### BPS states in omega background and integrability

- PhysicsJournal of High Energy Physics
- 2012

A bstractWe reconsider string and domain wall central charges in $ \mathcal{N} $ = 2 supersymmetric gauge theories in four dimensions in presence of the Omega background in the Nekrasov-Shatashvili…

### Bootstrapping the superconformal index with surface defects

- Mathematics
- 2013

A bstractThe analytic properties of the $ \mathcal{N}=2 $ superconformal index are given a physical interpretation in terms of certain BPS surface defects, which arise as the IR limit of…

### The virtue of defects in 4D gauge theories and 2D CFTs

- Mathematics
- 2011

We advance a correspondence between the topological defect operators in Liouville and Toda conformal field theories — which we construct — and loop operators and domain wall operators in four…

### Surface defects and instanton partition functions

- Mathematics
- 2014

A bstractWe study the superconformal index of five-dimensional SCFTs and the sphere partition function of four-dimensional gauge theories with eight supercharges in the presence of co-dimension two…

### Factorization of 4d N=1 superconformal index

- Physics, Mathematics
- 2014

We study the factorization of four dimensional N=1 superconformal index for U(N) (SU(N)) SQCD with N_F fundamental and anti-fundamental chiral multiplets. When both the anomaly free R-charge…