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

148

We give a unified approach to localization of maximally symmetric gauge theories on spheres, including S 6 and S 7 . The approach follows Pestun's method of dimensionally reducing from 10 dimensional super Yang-Mills. The resulting theories have a reduced R-symmetry which includes an SU(1, 1) subgroup, except in four dimensions where, because of conformal invariance, the full flat-space R-symmetry is maintained, and in seven dimensions where SU(1, 1) is the flat-space R-symmetry. For the case of S 6 and S 7 we discuss the localization of these theories and also present new results for the corresponding matrix models. The matrix models for S 6 and S 7 are qualitatively similar to the matrix models of a vector multiplet on S 4 and S 5 respectively. We also discuss the contributions of instantons in the six and seven dimensional cases.

Section: Jhep03(2015)155mentioning

confidence: 99%

Gauge theories with 16 supersymmetries on spheres

Minahan

Zabzine

2015

148

“…1 We are forced to use such an embedding because the six-dimensional N = (2, 0) theories are strongly coupled, and we do not know how to study them directly. 2 By embedding the six-dimensional theories into string theory backgrounds that are dual by the AdS/CFT correspondence to four-dimensional N = 2 SCFTs, we will be able to use the 'rigid holography' and the properties of these four-dimensional SCFTs to study the enigmatic six-dimensional theory. In particular, utilizing Gaiotto's description of S-duality, we will identify a subsector of these four-dimensional SCFTs (which decouples in an appropriate limit) that captures properties of the N = (2, 0) theory on AdS 5 × S 1 .…”

Section: Jhep03(2015)121mentioning

confidence: 99%

“…However, the Zamolodchikov metric for a weakly coupled gauge theory goes as: 2) so this implies that the origin of the 'moduli space' on AdS 5 (which we mapped to τ → i∞) is infinitely far away, see figure 7. 22 Furthermore, our discussion implies that the origin of the 'moduli space' is not just a point but a (K − 2)-dimensional space, corresponding to the parameter space of the P (K) theory.…”

Section: The Metric On the Moduli Spacementioning

confidence: 99%

“…In particular, on a set of compact curved spaces, the exact -twisted or refined -partition function and supersymmetric indices can be computed by localization techniques applied to various spacetime dimensions [1][2][3]. Comparatively, supersymmetric field theories on non-compact curved spaces were much less studied (see [4][5][6][7][8] for a few examples).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Rigid holography and six-dimensional N = 2 0 $$ \mathcal{N}=\left(2,0\right) $$ theories on AdS5 × S $$ \mathbb{S} $$ 1

Aharony

Berkooz

Rey

2015

Field theories on anti-de Sitter (AdS) space can be studied by realizing them as low-energy limits of AdS vacua of string/M theory. In an appropriate limit, the field theories decouple from the rest of string/M theory. Since these vacua are dual to conformal field theories, this relates some of the observables of these field theories on AdS space to a subsector of the dual conformal field theories. We exemplify this 'rigid holography' by studying in detail the six-dimensional N = (2, 0) A K−1 superconformal field theory (SCFT) on AdS 5 ×S 1 , with equal radii for AdS 5 and for S 1 . We choose specific boundary conditions preserving sixteen supercharges that arise when this theory is embedded into Type IIB string theory on AdS 5 × S 5 /Z K . On R 4,1 × S 1 , this six-dimensional theory has a 5(K − 1)-dimensional moduli space, with unbroken five-dimensional SU(K) gauge symmetry at (and only at) the origin. On AdS 5 × S 1 , the theory has a 2(K − 1)-dimensional 'moduli space' of supersymmetric configurations. We argue that in this case the SU(K) gauge symmetry is unbroken everywhere in the 'moduli space' and that this five-dimensional gauge theory is coupled to a four-dimensional theory on the boundary of AdS 5 whose coupling constants depend on the 'moduli'. This involves non-standard boundary conditions for the gauge fields on AdS 5 . Near the origin of the 'moduli space', the theory on the boundary contains a weakly coupled four-dimensional N = 2 supersymmetric SU(K) gauge theory. We show that this implies large corrections to the metric on the 'moduli space'. The embedding in string theory implies that the six-dimensional N = (2, 0) theory on AdS 5 × S 1 with sources on the boundary is a subsector of the large N limit of various four-dimensional N = 2 JHEP03(2015)121quiver SCFTs that remains non-trivial in the large N limit. The same subsector appears universally in many different four-dimensional N = 2 SCFTs. We also discuss a decoupling limit that leads to N = (2, 0) 'little string theories' on AdS 5 × S 1 .

“…The study of supersymmetric field theories on curved manifolds leads to new observables, which can often be calculated exactly using localization techniques [1][2][3][4][5][6][7][8]. Most authors have focused on supersymmetric theories with an R-symmetry.…”

Section: Introductionmentioning

confidence: 99%

Exploring curved superspace (II)

Dumitrescu

Festuccia

2013

129

We extend our previous analysis of Riemannian four-manifolds M admitting rigid supersymmetry to N = 1 theories that do not possess a U (1) R symmetry. With one exception, we find that M must be a Hermitian manifold. However, the presence of supersymmetry imposes additional restrictions. For instance, a supercharge that squares to zero exists, if the canonical bundle of the Hermitian manifold M admits a nowhere vanishing, holomorphic section. This requirement can be slightly relaxed if M is a torus bundle over a Riemann surface, in which case we obtain a supercharge that squares to a complex Killing vector. We also analyze the conditions for the presence of more than one supercharge.The exceptional case occurs when M is a warped product S 3 × R, where the radius of the round S 3 is allowed to vary along R. Such manifolds admit two supercharges that generate the superalgebra OSp(1|2).