5-dim superconformal index with enhanced E n global symmetry

165

We study N = 1 theories on Hermitian manifolds of the form M 4 = S 1 × M 3 with M 3 a U(1) fibration over S 2 , and their 3d N = 2 reductions. These manifolds admit an Heegaard-like decomposition in solid tori D 2 × T 2 and D 2 × S 1 . We prove that when the 4d and 3d anomalies are cancelled, the matrix integrands in the Coulomb branch partition functions can be factorised in terms of 1-loop factors on D 2 × T 2 and D 2 × S 1 respectively. By evaluating the Coulomb branch matrix integrals we show that the 4d and 3d partition functions can be expressed as sums of products of 4d and 3d holomorphic blocks.

Section: Jhep11(2015)155mentioning

confidence: 95%

Factorisation and holomorphic blocks in 4d

Nieri

Pasquetti

2015

165

“…By appropriate vevs which break the gauge groups as SU(k) → U(k − 1), the theory can be reduced to a quiver 33) where all the bifundamentals are massless. It is standard that tr µ k A = 0 and µ N −1 A = 0 follow from the F-term conditions, see e.g.…”

Section: Jhep02(2015)089mentioning

confidence: 99%

“…The tuning conditions may be deduced from the location of simple poles in the 5d superconformal index (or the 5d partition function on S 4 × S 1 ) of the theory [10,32]. The 5d superconformal index of a superconformal field theory can be computed by the localization technique [33], and it is obtained by the integration over holonomy variables corresponding to Coulomb branch moduli and the integrand is the product of the contributions localized at the north JHEP02 (2015)089 pole and the south pole of S 4 . Those contributions are nothing but the 5d Nekrasov partition functions 4 of the theory, and hence once we know the 5d partition function, we can compute the corresponding 5d superconformal index.…”

Section: Higgsing One Full Puncturementioning

confidence: 99%

Mass-deformed T N as a linear quiver

Hayashi

Tachikawa

Yonekura

2015

Abstract:The T N theory is a non-Lagrangian theory with SU(N ) 3 flavor symmetry. We argue that when mass terms are given so that two of SU(N )'s are both broken to SU(N −1)×U(1), it becomes T N −1 theory coupled to an SU(N −1) vector multiplet together with N fundamentals. This implies that when two of SU(N )'s are both broken to U(1) N −1 , the theory becomes a linear quiver.We perform various checks of this statement, by using the 5d partition function, the structure of the coupling constants, the Higgs branch, and the Seiberg-Witten curve. We also study the case with more general punctures.

“…It has been expected for a long time that these theories have an UV fixed point where the global symmetry is enhanced to E N f +1 [6][7][8][9]. The enhancement of the global symmetries is supported from the computation of the fivedimensional superconformal index [10][11][12]. It is clear therefore that using webs of 5-branes it is possible to realise a large class of five-dimensional superconformal field theories.…”

Section: Jhep09(2015)023mentioning

confidence: 78%

“…The dual gauge group on the k D0-branes for the Sp(N ) gauge theory is O(k), which have two components. Hence, we have two contributions Z k ± from O(k) ± at each instanton order, and the end result from k-instanton is written by [10,12] …”

Section: C1 Sp(n ) Instanton Partition Functionsmentioning

confidence: 99%

Topological vertex for Higgsed 5d T N theories

Hayashi

Zoccarato

2015

Abstract:We analyse the computation of the partition function of 5d T N theories in Higgs branches using the topological vertex. The theories are realised by a web of (p, q) 5-branes whose dual description may be given by an M-theory compactification on a certain local non-toric Calabi-Yau threefold. We explicitly show how it is possible to directly apply the topological vertex to the non-toric geometry. Using this novel technique, which considerably simplifies the computation by the existing method, we are able to compute the partition function of the higher rank E 6 , E 7 and E 8 theories. Moreover we show how in some specific cases similar results can be extended to the computation of the partition function of 5d T N theories in the Higgs branch using the refined topological vertex. These cases require a modification of the refined topological vertex.