Takahiro Nishinaka

Topological strings and 5d T N partition functions

A bstractWe evaluate the Nekrasov partition function of 5d gauge theories engineered by webs of 5-branes, using the refined topological vertex on the dual Calabi-Yau three-folds. The theories include certain non-Lagrangian theories such as the TN theory. The refined topological vertex computation generically contains contributions from decoupled M2-branes which are not charged under the 5d gauge symmetry engineered. We argue that, after eliminating them, the refined topological string partition function agrees with the 5d Nekrasov partition function. We explicitly check this for the T3 theory as well as Sp(1) gauge theories with Nf = 2, 3, 4 flavors. In particular, our method leads to a new expression of the Sp(1) Nekrasov partition functions without any contour integrals. We also develop prescriptions to calculate the partition functions of theories obtained by Higgsing the TN theory. We compute the partition function of the E7 theory via this prescription, and find the E7 global symmetry enhancement. We finally discuss a potential application of the refined topological vertex to non-toric web diagrams.

On the superconformal index of Argyres–Douglas theories

We conjecture a closed-form expression for the Schur limit of the superconformal index of two infinite series of Argyres-Douglas (AD) superconformal field theories (SCFTs): the (A1,A2n−3) and the (A1,D2n) theories. While these SCFTs can be realized at special points on the Coulomb branch of certain N = 2 gauge theories, their superconformal R symmetries are emergent, and hence their indices cannot be evaluated by localization. Instead, we construct the (A1,A2n−3) and (A1,D2n) indices by using a relation to two-dimensional qdeformed Yang-Mills theory and data from the class S construction. Our results generalize the indices derived from the torus partition functions of the two-dimensional chiral algebras associated with the (A1,A3) and (A1,D4) SCFTs. As checks of our conjectures, we study the consistency of our results with an S-duality recently discussed by us in collaboration with Giacomelli and Papageorgakis, we reproduce known Higgs branch relations, we check consistency with a series of renormalization group flows, and we verify that the small S 1 limits of our indices reproduce expected Cardy-like behavior. We will discuss the S 1

The CFT-interpolating black hole in three dimensions

We present a new exact black hole solution in three dimensional Einstein gravity coupled to a single scalar field. This is one of the extended solutions of the BTZ black hole and has in fact AdS3 geometries both at the spatial infinity and at the event horizon. An explicit derivation of Virasoro algebras for CFT2 at the two boundaries is shown to be possible ? la Brown and Henneauxs calculation. If we regard the scalar field as a running coupling in the dual two dimensional field theory, and its flow in the bulk as the ``holographic renormalization group flow, our black hole should interpolate the two CFT2 living at the infinity and at the horizon. Following the Hamilton-Jacobi analysis by de Boer, Verlinde and Verlinde, we calculate the central charges cUV and cIR for the CFT2 on the infinity and the horizon, respectively. We also confirm that the inequality cIR < cUV is satisfied, which is consistent with the Zamolodchikovs c-theorem.

Constraints on chiral operators in N = 2 SCFTs

A bstractWe study certain higher-spin chiral operators in N=2

Argyres-Douglas theories, the Macdonald index, and an RG inequality

\mathcal{N}=2

Argyres–Douglas theories, S 1 reductions, and topological symmetries

superconformal field theories (SCFTs). In Lagrangian theories, or in theories related to Lagrangian theories by generalized Argyres-Seiberg-Gaiotto duality (“type A” theories in our classification), we give a simple superconformal representation theory proof that such operators do not exist. This argument is independent of the details of the superconformal index. We then use the index to show that if a theory is not of type A but has an N=2

On 4d rank-one \( \mathcal{N}=3 \) superconformal field theories

\mathcal{N}=2