Related papers: Partition functions of web diagrams with an O7$^-$…
We study the perturbative large-$N$ expansion of the round three-sphere partition function in a class of M2-brane theories, including flavored SYM and ABJM theories as well as more general 3d theories admitting dual $(p,q)$ 5-brane web…
We study webs of 5-branes with 7-branes in Type IIB string theory from a geometric perspective. Mathematically, a web of 5-branes with 7-branes is a tropical curve in $\mathbb{R}^2$ with focus-focus singularities introduced. To any such a…
We consider BPS-counting functions $\mathcal{Z}_{N,M}$ of $N$ parallel M5-branes probing a transverse $\mathbb{Z}_M$ orbifold geometry. These brane web configurations can be dualised into a class of toric non-compact Calabi-Yau threefolds…
We show that the three different looking BPS partition functions, namely the elliptic genus of the 6d $\mathcal{N}=(1,0)$ $Sp(1)$ gauge theory with $10$ flavors and a tensor multiplet, the Nekrasov partition function of the 5d…
We derive the exact vortex partition function in 2d $\mathcal{N}$ = (2,2) gauge theory on the Omega-background, applying the localization scheme in the Higgs phase. We show that the partition function at a finite Omega-deformation parameter…
In this note we investigate certain topological aspects of the effective action of the NS5-brane in type IIA string theory. To facilitate the study of the corresponding partition function, we define a cohomology class whose vanishing is a…
We calculate the topological string partition function to all genus on the conifold, in the presence of branes. We demonstrate that the partition functions for different brane backgrounds (smoothly connected along a quantum corrected moduli…
We consider M-theory in the presence of M parallel M5-branes probing a transverse A_{N-1} singularity. This leads to a superconformal theory with (1,0) supersymmetry in six dimensions. We compute the supersymmetric partition function of…
We propose a novel string theory propagating in a non-commutative deformation of the four dimensional space T* T^2 whose scattering states correspond to superconformal theories in 5 dimensions and the scattering amplitudes compute…
The partition function of type IIA and B strings on R^6xK3, in the T^4/Z_2 orbifold limit, is explicitly computed as a modular invariant sum over spin strutures required by perturbative unitarity in order to extend the analysis to include…
We derive the partition function of 5d ${\cal N}=1$ gauge theories on the manifold $S^3_b \times \Sigma_{\frak g}$ with a partial topological twist along the Riemann surface, $\Sigma_{\frak g}$. This setup is a higher dimensional uplift of…
We explore the properties of five-dimensional supersymmetric gauge theories living on 5-brane webs in orientifold 7-plane backgrounds. These include $USp(2N)$ and $SO(N)$ gauge theories with fundamental matter, as well as $SU(N)$ gauge…
Worldsheet string theory is solvable for a variety of backgrounds involving Neveu-Schwarz fivebranes, in terms of gauged nonlinear sigma models on group manifolds. We compute the worldsheet torus partition function of these models, and…
Partition functions for M2-brane theories in various backgrounds are computed. We consider in particular configurations of membranes at orbifold singularities preserving N=5 or N=6 supersymmetry. The worldvolume membrane theory for some of…
It is known that a 4d N = 1 SCFT lives on D3-branes probing a local del Pezzo Calabi-Yau singularity. The Seiberg (or toric) duality of this SCFT arises from the Picard-Lefshetz transformation of the affine E_N 7-brane background that is…
We derive a family of matrix models which encode solutions to the Seiberg-Witten theory in 4 and 5 dimensions. Partition functions of these matrix models are equal to the corresponding Nekrasov partition functions, and their spectral curves…
The topological vertex formalism for 5d $\mathcal{N}=1$ gauge theories is not only a convenient tool to compute the instanton partition function of these theories, but it is also accompanied by a nice algebraic structure that reveals…
In this paper we use the the topological vertex formalism to calculate a generalization of the "domain wall" partition function of M-strings. This generalization allows calculation of partition function of certain compactified webs using a…
We study 5d $\mathcal{N}=1$ supersymmetric field theories on closed five-manifolds $\mathcal{M}_5$ which are principal circle bundles over simply-connected K\"ahler four-manifolds, $\mathcal{M}_4$, equipped with the Donaldson-Witten twist.…
We propose 5d descriptions of 6d ${\cal N}=(1,0)$ superconformal field theories arising from Type IIA brane configurations with an $O8^-$-plane. We T-dualize the brane diagram along a compactification circle and obtain a 5-brane web diagram…