We study the correlation functions of Coulomb branch operators of four-dimensional $$ \mathcal{N} $$ N = 2 Superconformal Field Theories (SCFTs). We focus on rank-one theories, such as the SU(2) gauge theory with four fundamental hypermultiplets. “Extremal” correlation functions, involving exactly one anti-chiral operator, are perhaps the simplest nontrivial correlation functions in four-dimensional Quantum Field Theory. We show that the large charge limit of extremal correlators is captured by a “dual” description which is a chiral random matrix model of the Wishart-Laguerre type. This gives an analytic handle on the physics in some particular excited states. In the limit of large random matrices we find the physics of a non-relativistic axion-dilaton effective theory. The random matrix model also admits a ’t Hooft expansion in which the matrix is taken to be large and simultaneously the coupling is taken to zero. This explains why the extremal correlators of SU(2) gauge theory obey a nontrivial double scaling limit in states of large charge. We give an exact solution for the first two orders in the ’t Hooft expansion of the random matrix model and compare with expectations from effective field theory, previous weak coupling results, and we analyze the non-perturbative terms in the strong ’t Hooft coupling limit. Finally, we apply the random matrix theory techniques to study extremal correlators in rank-1 Argyres-Douglas theories. We compare our results with effective field theory and with some available numerical bootstrap bounds.

In this paper we summarise the localisation calculation of 5D super Yang-Mills on simply connected toric Sasaki-Einstein (SE) manifolds. We show how various aspects of the computation, including the equivariant index, the asymptotic behaviour and the factorisation property are governed by the combinatorial data of the toric geometry. We prove that the full perturbative partition function on a simply connected SE manifold corresponding to an n-gon toric diagram factorises to n copies of perturbative Nekrasov partition function. This leads us to conjecture the full partition function as gluing n copies of full Nekrasov partition function. This work is a generalisation of some earlier computation carried out on Y p,q manifolds, whose moment map cone has a quadrangle and our result is valid for manifolds whose moment map cones have pentagon base, hexagon base, etc. The algorithm we used for dealing with general cones may also be of independent interest.

One of the hallmarks of 6D superconformal field theories (SCFTs) is that on a partial tensor branch, all known theories resemble quiver gauge theories with links comprised of 6D conformal matter, a generalization of weakly coupled hypermultiplets. In this paper we construct 4D quiverlike gauge theories in which the links are obtained from compactifications of 6D conformal matter on Riemann surfaces with flavor symmetry fluxes. This includes generalizations of super QCD with exceptional gauge groups and quarks replaced by 4D conformal matter. Just as in super QCD, we find evidence for a conformal window as well as confining gauge group factors depending on the total amount of matter. We also present Ftheory realizations of these field theories via elliptically fibered Calabi-Yau fourfolds. Gauge groups (and flavor symmetries) come from 7-branes wrapped on surfaces, conformal matter localizes at the intersection of pairs of 7-branes, and Yukawas between 4D conformal matter localize at points coming from triple intersections of 7-branes. Quantum corrections can also modify the classical moduli space of the F-theory model, matching expectations from effective field theory.

We present a 6D generalization of the fractional quantum Hall effect involving membranes coupled to a three-form potential in the presence of a large background four-form flux. The low energy physics is governed by a bulk 7D topological field theory of abelian threeform potentials with a single derivative Chern-Simons-like action coupled to a 6D anti-chiral theory of Euclidean effective strings. We derive the fractional conductivity, and explain how continued fractions which figure prominently in the classification of 6D superconformal field theories correspond to a hierarchy of excited states. Using methods from conformal field theory we also compute the analog of the Laughlin wavefunction. Compactification of the 7D theory provides a uniform perspective on various lower-dimensional gapped systems coupled to boundary degrees of freedom. We also show that a supersymmetric version of the 7D theory embeds in M-theory, and can be decoupled from gravity. Encouraged by this, we present a conjecture in which IIB string theory is an edge mode of a 10 + 2-dimensional bulk topological theory, thus placing all twelve dimensions of F-theory on a physical footing.

We propose a stringy construction giving rise to a class of interacting and non-supersymmetric CFT's in six dimensions. Such theories may be obtained as an IR conformal fixed point of an RG flow ending up in a (1, 0) theory in the UV. We provide the due holographic evidence in the context of massive type IIA on AdS 7 × M 3 , where M 3 is topologically an S 3 . In particular, in this paper we present a 10d flow solution which may be interpreted as a non-BPS bound state of NS5, D6 and D6 branes. Moreover, by adopting its 7d effective description, we are able to holographically compute the free energy and the operator spectrum in the novel IR conformal fixed point.

All five-dimensional non-abelian gauge theories have a U(1)I global symmetry associated with instantonic particles. We describe an obstruction to coupling U(1)I to a classical background gauge field that occurs whenever the theory has a one-form center symmetry. This is a finite-order mixed ’t Hooft anomaly between the two symmetries. We also show that a similar obstruction takes place in gauge theories with fundamental matter by studying twisted bundles for the ordinary flavor symmetry. We explore some general dynamical properties of the candidate phases implied by the anomaly. Finally, we apply our results to supersymmetric gauge theories in five dimensions and analyze the symmetry enhancement patterns occurring at their conjectured RG fixed points.

We revisit the confinement/deconfinement transition in $$ \mathcal{N} $$ N = 4 super Yang-Mills (SYM) theory and its relation to the Hawking-Page transition in gravity. Recently there has been substantial progress on counting the microstates of 1/16-BPS extremal black holes. However, there is presently a mismatch between the Hawking-Page transition and its avatar in $$ \mathcal{N} $$ N = 4 SYM. This led to speculations about the existence of new gravitational saddles that would resolve the mismatch. Here we exhibit a phenomenon in complex matrix models which we call “delayed deconfinement.” It turns out that when the action is complex, due to destructive interference, tachyonic modes do not necessarily condense. We demonstrate this phenomenon in ordinary integrals, a simple unitary matrix model, and finally in the context of $$ \mathcal{N} $$ N = 4 SYM. Delayed deconfinement implies a first-order transition, in contrast to the more familiar cases of higher-order transitions in unitary matrix models. We determine the deconfinement line and find remarkable agreement with the prediction of gravity. On the way, we derive some results about the Gross-Witten-Wadia model with complex couplings. Our techniques apply to a wide variety of (SUSY and non-SUSY) gauge theories though in this paper we only discuss the case of $$ \mathcal{N} $$ N = 4 SYM.

We study various aspects of global symmetries in five-dimensional superconformal field theories. Whenever a supersymmetry-preserving relevant deformation is available, the infrared gauge theory description might exhibit a finite order mixed 't Hooft anomaly between a 1-form symmetry and the instantonic symmetry. This anomaly constrains the flavor symmetry group acting faithfully on the SCFT and the consistency of certain RG flows. As an additional example, we consider the instructive case of three-dimensional N = 4 SQED. Finally, we discuss the compatibility between conformal invariance and the presence of 1-form and 2-group global symmetries.