From 4d superconformal indices to 3d partition functions

Dolan, F.A.; Spiridonov, V. P.; Vartanov, G. S.

doi:10.1016/j.physletb.2011.09.007

Cited by 149 publications

(202 citation statements)

References 43 publications

Supporting

Mentioning

195

Contrasting

Unclassified

Order By: Relevance

“…However, the "high temperature" limit for indices, β → 0, or equivalently ω 2 → ∞, or p → 1 and q → 1, is well known. As noticed first in [24], in this case the indices reduce to partition functions of three-dimensional field theories up to a diverging exponential, which was shown in [40] to be related to anomaly coefficients in the combination a − c. The results of [21] were applied also in the context of formal holomorphic block factorisations of 4d superconformal indices [41] with the corresponding β → 0 3d-reduction. A more detailed consideration of this limit for several different theories was given in [42].…”

Section: Jhep07(2017)041mentioning

confidence: 90%

“…In particular, there exists a transformation that partially relates the high and low "temperature" 1 asymptotics of the indices. The high temperature limit, when both basic parameters p and q tend to 1, maps indices to the hyperbolic integrals describing three-dimensional partition functions [24], while the low temperature limit, when p and q go to zero, degenerates the indices to Hilbert series counting the gauge invariant operators [25,26]. The intermediate case, when only one of JHEP07(2017)041 the base parameters p or q goes to zero, reduces to the Macdonald theory -a relation which was noticed first in [27] and later developed in detail in [28].…”

Section: Jhep07(2017)041mentioning

confidence: 99%

See 1 more Smart Citation

Supersymmetric Casimir energy and S L 3 ℤ $$ \mathrm{S}\mathrm{L}\left(3,\mathrm{\mathbb{Z}}\right) $$ transformations

Brünner

Regalado

Spiridonov

2017

J. High Energ. Phys.

View full text Add to dashboard Cite

We provide a recipe to extract the supersymmetric Casimir energy of theories defined on primary Hopf surfaces directly from the superconformal index. It involves an SL(3, Z) transformation acting on the complex structure moduli of the background geometry. In particular, the known relation between Casimir energy, index and partition function emerges naturally from this framework, allowing rewriting of the latter as a modified elliptic hypergeometric integral. We show this explicitly for N = 1 SQCD and N = 4 supersymmetric Yang-Mills theory for all classical gauge groups, and conjecture that it holds more generally. We also use our method to derive an expression for the Casimir energy of the nonlagrangian N = 2 SCFT with E 6 flavour symmetry. Furthermore, we predict an expression for Casimir energy of the N = 1 SP(2N) theory with SU(8) × U(1) flavour symmetry that is part of a multiple duality network, and for the doubled N = 1 theory with enhanced E 7 flavour symmetry.

show abstract

Section: Jhep07(2017)041mentioning

confidence: 90%

Section: Jhep07(2017)041mentioning

confidence: 99%

Supersymmetric Casimir energy and S L 3 ℤ $$ \mathrm{S}\mathrm{L}\left(3,\mathrm{\mathbb{Z}}\right) $$ transformations

Brünner

Regalado

Spiridonov

2017

J. High Energ. Phys.

View full text Add to dashboard Cite

show abstract

“…Since y = 1 corresponds to a computation of the supersymmetric partition function on the round S 3 [27][28][29], we see that no squashing is needed to have a and c separately encoded. One can also turn Eq.…”

Section: Moving Away From Large-nmentioning

confidence: 97%

Central Charges from theN=1Superconformal Index

2015

View full text Add to dashboard Cite

We present prescriptions for obtaining the central charges, a and c, of a four dimensional superconformal quantum field theory from the superconformal index. At infinite N , for holographic theories dual to Sasaki-Einstein 5-manifolds the prescriptions give the O(1) parts of the central charges. This allows us, among other things, to show the exact AdS/CFT matching of a and c for arbitrary toric quiver CFTs without adjoint matter that are dual to smooth Sasaki-Einstein 5-manifolds. In addition, we include evidence from non-holographic theories for the applicability of these results outside of a holographic setting and away from the large-N limit.

show abstract

“…They can be realized by reducing the complex structure and the Hermitian metric (4.7) on primary Hopf surfaces M p,q 4 along ∂ x . (Various reductions from S 3 × S 1 to squashed three-spheres were discussed in [44,45,54,73,74].) Since this family of THFs is one-dimensional, the corresponding partition functions Z S 3 should only depend on the geometry through a single complex parameter -the squashing parameter b.…”

Section: Jhep01(2014)124mentioning

confidence: 99%

The geometry of supersymmetric partition functions

Closset

Dumitrescu

Festuccia

et al. 2014

J. High Energ. Phys.

172

415

View full text Add to dashboard Cite

We consider supersymmetric field theories on compact manifolds M and obtain constraints on the parameter dependence of their partition functions Z M . Our primary focus is the dependence of Z M on the geometry of M, as well as background gauge fields that couple to continuous flavor symmetries. For N = 1 theories with a U(1) R symmetry in four dimensions, M must be a complex manifold with a Hermitian metric. We find that Z M is independent of the metric and depends holomorphically on the complex structure moduli. Background gauge fields define holomorphic vector bundles over M and Z M is a holomorphic function of the corresponding bundle moduli. We also carry out a parallel analysis for three-dimensional N = 2 theories with a U(1) R symmetry, where the necessary geometric structure on M is a transversely holomorphic foliation (THF) with a transversely Hermitian metric. Again, we find that Z M is independent of the metric and depends holomorphically on the moduli of the THF. We discuss several applications, including manifolds diffeomorphic to S 3 ×S 1 or S 2 ×S 1 , which are related to supersymmetric indices, and manifolds diffeomorphic to S 3 (squashed spheres). In examples where Z M has been calculated explicitly, our results explain many of its observed properties.

show abstract

From 4d superconformal indices to 3d partition functions

Cited by 149 publications

References 43 publications

Supersymmetric Casimir energy and S L 3 ℤ $$ \mathrm{S}\mathrm{L}\left(3,\mathrm{\mathbb{Z}}\right) $$ transformations

Supersymmetric Casimir energy and S L 3 ℤ $$ \mathrm{S}\mathrm{L}\left(3,\mathrm{\mathbb{Z}}\right) $$ transformations

Central Charges from theN=1Superconformal Index

The geometry of supersymmetric partition functions

Contact Info

Product

Resources

About