Superconformal indices of three-dimensional theories related by mirror symmetry

@article{Krattenthaler2011SuperconformalIO,
  title={Superconformal indices of three-dimensional theories related by mirror symmetry},
  author={Christian Krattenthaler and Vyacheslav P. Spiridonov and Grigory S. Vartanov},
  journal={Journal of High Energy Physics},
  year={2011},
  volume={2011},
  pages={1-20}
}
Recently, Kim, and Imamura and Yokoyama derived an exact formula for superconformal indices in three-dimensional field theories. Using their results, we prove analytically the equality of superconformal indices in some U(1)-gauge group theories related by mirror symmetry. The proofs are based on well-known identities in the theory of q-special functions. We also suggest a general index formula taking into account the U(1)J global symmetry present for abelian theories. 

Index for Three Dimensional Superconformal Field Theories and Its Applications

We review aspects of superconformal indices in three dimension. Three dimensional superconformal indices can be exactly computed by using localization method including monopole contribution, and can

Index for three dimensional superconformal field theories with general R-charge assignments

We derive a general formula of an index for three dimensional $ \mathcal{N} = 2 $ super-conformal field theories with general R-charge assignments to chiral multiplets by using the localization

Superconformal indices, dualities and integrability

In this thesis we discuss exact, non-perturbative results achieved using superconformal index technique in supersymmetric gauge theories with four supercharges (which is N = 1 supersymmetry in four

Generalized Superconformal Index for Three Dimensional Field Theories

We introduce a generalization of the S^2 × S^1 superconformal index where background gauge fields with magnetic flux are coupled to the global symmetries of the theory. This allows one to gauge a

The star-triangle relation and 3d superconformal indices

Superconformal indices of 3d N = 2 supersymmetric field theories are investigated from the Yang-Baxter equation point of view. Solutions of the star-triangle relation, vertex and IRF Yang-Baxter

Superconformal index on RP 2 × S 1 and 3 d mirror symmetry

In three dimensional quantum field theory, it is known that there is a nontrivial duality called 3d mirror symmetry. To check the duality, the so-called superconformal index is known to be a powerful

Integral pentagon relations for 3d superconformal indices

The superconformal index of a three-dimensional supersymmetric field theory can be expressed in terms of basic hypergeometric integrals. By comparing the indices of dual theories, one can find new

Pentagon Identities Arising in Supersymmetric Gauge Theory Computations

The partition functions of three-dimensional N=2 supersymmetric gauge theories on different manifolds can be expressed as q-hypergeometric integrals. Comparing the partition functions of

On three-dimensional quiver gauge theories of type B

A bstractWe study three-dimensional supersymmetric quiver gauge theories with a nonsimply laced global symmetry primarily focusing on framed affine BN quiver theories. Using a supersymmetric

Single-flavor Abelian mirror symmetry on ℝℙ2 × S1

The superconformal index on ℝℙ2 × S1 can be derived exactly by the localization technique and applied to the direct proof of Abelianmirror symmetry. We find two sets of parity conditions compatible
...

References

SHOWING 1-10 OF 49 REFERENCES

Superconformal indices for orbifold Chern-Simons theories

We calculate the superconformal indices of recently discovered three-dimensional N = 4,5 Chern-Simons-matter theories and compare them with the corresponding indices of supergravity on AdS4 times

Index for three dimensional superconformal field theories with general R-charge assignments

We derive a general formula of an index for three dimensional $ \mathcal{N} = 2 $ super-conformal field theories with general R-charge assignments to chiral multiplets by using the localization

Calculating the Superconformal Index and Seiberg Duality

We develop techniques to calculate an index for four dimensional superconformal field theories. This superconformal index is counting BPS operators which preserve only one supercharge. To calculate

Superconformal index for large N quiver Chern-Simons theories

We investigate the $ \mathcal{N} = 2 $ superconformal index for supersymmetric quiver Chern-Simons theories with large N gauge groups. After general arguments about the large N limit, we compute the

The exact superconformal R-symmetry extremizes Z

A bstractThe three sphere partition function, Z , of three dimensional theories with four supercharges and an R-symmetry is computed using localization, resulting in a matrix integral over the Cartan

Superconformal Indices for N = 6 Chern Simons Theories

Aharony, Bergman, Jafferis and Maldacena have recently proposed a dual gravitational description for a family of superconformal Chern Simons theories in three spacetime dimensions. In this note we

Indices for superconformal field theories in 3, 5 and 6 dimensions

We present a trace formula for a Witten type Index for superconformal field theories in d = 3, 5 and 6 dimensions, generalizing a similar recent construction in d = 4. We perform a detailed study of

Nonperturbative tests of three-dimensional dualities

We test several conjectural dualities between strongly coupled superconformal field theories in three dimensions by computing their exact partition functions on a three sphere as a function of

Exact results for Wilson loops in superconformal Chern-Simons theories with matter

We use localization techniques to compute the expectation values of supersymmetric Wilson loops in Chern-Simons theories with matter. We find the path-integral reduces to a non-Gaussian matrix model.