Related papers: O-vertex, O7$^+$-plane, and Topological Vertex
Searching for the integrable structures of supersymmetric gauge theories and topological strings, we study melting crystal, which is known as random plane partition, from the viewpoint of integrable systems. We show that a series of…
We show that the $\mathcal{N}=(1,0)$ superconformal theory on a single M5 brane on the ALE space of type $G=A_n, D_n, E_n$, when compactified on $T^2$, becomes a class S theory of type $G$ on a sphere with two full punctures and a simple…
We construct cobordism maps for the \textit{minus} version of instanton knot homology associated to a \textit{specially decorated} knot cobordisms of arbitrary genus between two null-homologous knots in closed oriented $3$-manifolds. As an…
We propose new ADHM-like methods to compute the Coulomb branch instanton partition functions of 5d and 6d supersymmetric gauge theories, with certain exceptional gauge groups or exceptional matters. We study $G_2$ theories with $n_{\bf…
We study $6$d $\mathcal{N} = (1,0)$ supergravity theories arising in the frozen phase of F-theory. For each of the known global models, we construct an F-theory compactification in the unfrozen phase with an identical non-abelian gauge…
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 use the 5-sphere partition functions of supersymmetric Yang-Mills theories to explore the (2,0) superconformal theory on S^5 x S^1. The 5d theories can be regarded as Scherk-Schwarz reductions of the 6d theory along the circle. In a…
We present a structural resolution to the exact evaluation of the partition function $p_k(n)$, systematically overcoming the limitations of traditional recursive and asymptotic methods. By framing the partition polytope $\mathcal{P}_{n,k}$…
We study the octonionic selfduality equations for $p=3$-branes in the light cone gauge and we construct explicitly, instanton solutions for spherical and toroidal topologies in various flat spacetime dimensions $(D=5+1,7+1,8+1,9+1)$,…
Motivated by physical constructions of homological knot invariants, we study their analogs for closed 3-manifolds. We show that fivebrane compactifications provide a universal description of various old and new homological invariants of…
We study the Type IIA NS five-brane wrapped on a Calabi-Yau manifold X in a double-scaled decoupling limit. We calculate the euclidean partition function in the presence of a flat RR 3-form field. The classical contribution is given by a…
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…
M-theory frozen singularities are (locally) $D$- or $E$-type orbifold singularities with a background fractional $C_3$-monodromy surrounding them. In this paper, we revisit such backgrounds and address several puzzling features of their…
We propose a non-perturbative definition for refined topological strings. This can be used to compute the partition function of superconformal theories in 5 dimensions on squashed S^5 and the superconformal index of a large number of 6…
We glue four refined topological vertices to obtain the building block of 5D $U(2)$ quiver instanton partition functions. We take the 4D limit of the result to obtain the building block of 4D instanton partition functions which, using the…
Building on recent progress in the study of compactifications of $6d$ $(1,0)$ superconformal field theories (SCFTs) on Riemann surfaces to $4d$ $\mathcal{N}=1$ theories, we initiate a systematic study of compactifications of $5d$…
Nekrasov's partition function is defined on a flat bundle of R^4 over S^1 called the Omega background. When the fibration is self-dual, the partition function is known to be equal to the topological string partition function, which computes…
Quiver 5D $\mathcal{N}=1$ gauge theories describe the low-energy dynamics on webs of $(p,q)$-branes in type IIB string theory. S-duality exchanges NS5 and D5 branes, mapping $(p,q)$-branes to branes of charge $(-q,p)$, and, in this way,…
We propose a new 5d description of the circle-compactified 6d $(D_{N+4}, D_{N+4})$ minimal conformal matter theory which can be approached by the 6d $\mathcal{N}=(1,0)$ $Sp(N)$ gauge theory with $N_f=2N+8$ flavors and one tensor multiplet.…
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…