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We study N=2 supersymmetric four dimensional gauge theories, in a certain N=2 supergravity background, called Omega-background. The partition function of the theory in the Omega-background can be calculated explicitly. We investigate…
Large classes of warped AdS$_6$ solutions were constructed recently in Type IIB supergravity, and identified as holographic duals for five-dimensional superconformal field theories realized by $(p,q)$ five-brane webs. We confront…
We develop a non planar topological vertex formalism and we use it to study the A-model partition function $\mathcal{Z}_{top}$ of topological string on the class of toric Calabi-Yau threefolds (CY3) in large complex structure limit. To that…
We derive the relation between the Hilbert space of certain geometries under the Bohr-Sommerfeld quantization and the perturbative prepotentials for the supersymmetric five-dimensional SU(N) gauge theories with massive fundamental matters…
We study the equivariant generalization of topological strings on toric manifolds, focusing in particular on defining the contributions of constant maps in the genus expansion of the partition function. This approach regularizes the…
The ALE partition functions of a 6d (1,0) SCFT are interesting observables which are able to detect the global structure of the SCFT. They are defined to be the equivariant partition functions of the SCFT on a background with the topology…
We study four-dimensional N=1 gauge theories arising on D3-branes probing toric singularities. Toric dualities and flows between theories corresponding to different singularities are analyzed by encoding the geometric information into (p,q)…
Worldsheet (0,2) gauged linear sigma models are often used to study supersymmetric heterotic string compactifications with non-trivial vector bundles. We make use of supersymmetric localization techniques to determine their one-loop…
We discuss what topological data must be provided to define topologically twisted partition functions of four-dimensional $\mathcal{N}=2$ supersymmetric field theories. The original example of Donaldson-Witten theory depends only on the…
D3-/D5-/NS5-brane systems with $O3$ orientifold planes realise 3d $\mathcal{N}=4$ gauge theories with orthogonal and symplectic gauge groups on the D3-brane worldvolume. Such setups have long contained an ambiguity regarding the global form…
We present the unrefined instanton partition functions of various 5d gauge theories with matter beyond the fundamental representation as sums over Young diagrams. By using these explicit expressions, we verify a range of identities among…
$\mathbb{Z}_n$ S-folds of 5d SCFTs, including $T_N$, which lead to brane webs with $E_{6,7,8}$ 7-branes were discussed recently. We generalize the construction to `fractional quotients', which are based on $\mathbb{Z}_n$ actions linking…
We consider the equations of motion of the non-abelian 5-branes theory recently constructed in http://arxiv.org/abs/arXiv:1203.4224 and find exact string solutions both for uncompactified and compactified spacetime. Although one does not…
We extend the recent study of 3d tt* geometry to 5d (4d) N=1 (N=2) supersymmetric theories. We show how the amplitudes of tt* geometry lead to an extension of topological strings and Nekrasov partition functions to twistor space, where the…
We propose two novel methods for computing the superconformal index of 5d superconformal field theories that cannot be described by conventional Lagrangian descriptions under mass deformations. The first approach involves the use of Higgs…
S-folds are a non-perturbative generalization of orientifold 3-planes which figure prominently in the construction of 4D $\mathcal{N} = 3$ SCFTs and have also recently been used to realize examples of 4D $\mathcal{N} = 2$ SCFTs. In this…
We connect the indications of 2D CFT for branes in non-supersymmetric strings to actual spacetime profiles, taking the bulk tadpole potentials into account. We find exact solutions for the uncharged branes that spread in the internal…
We study the partition function of type IIA string theory on 10-manifolds of the form T^2 x X where X is 8-dimensional, compact, and spin. We pay particular attention to the effects of the topological phases in the supergravity action…
Itoyama-Tokura type USp matrix model is discussed. Non-Abelian Berry's phases in a T-dualized model of IT model were reconsidered. These phases describe the higher dimensional monopoles; Yang monopole and nine-dimensional monopole. They are…
We examine compactifications of heterotic string theory on manifolds with SU(3) structure. In particular, we study N = 1/2 domain wall solutions which correspond to the perturbative vacua of the 4D, N =1 supersymmetric theories associated…