Related papers: Blowups in BPS/CFT correspondence, and Painlev\'e …

Blowup equations and holomorphic anomaly equations are two universal yet completely different approaches to solve refined topological string theory on local Calabi-Yau threefolds corresponding to A- and B-model respectively. The former…

We analyse a blow-up sequence of solutions for Liouville type equations involving Dirac measures with "collapsing" poles. We consider the case where blow-up occurs exactly at a point where the poles coalesce. After proving that a…

We compute the exact path integral of $\mathcal{N}=2$ supersymmetric gauge theories with general gauge group on $\mathbb{RP}^4$ and a $\mathbb{Z}_2$-quotient of the hemi-$S^4$. By specializing to $SU(2)$ superconformal quivers, we show that…

We give a notion of BV function on an oriented manifold where a volume form and a family of lower semicontinuous quadratic forms $G_p: T_pM \to [0,\infty]$ are given. When we consider sub-Riemannian manifolds, our definition coincide with…

Generic c=1 four-point conformal blocks on the Riemann sphere can be seen as the coefficients of Fourier expansion of the tau function of Painlev\'e VI equation with respect to one of its integration constants. Based on this relation, we…

We propose an interesting BPS/CFT correspondence playground: the correlation function of two intersecting half-BPS surface defects in four-dimensional $\mathcal{N}=2$ supersymmetric $SU(N)$ gauge theory with $2N$ fundamental…

F-theory compactifications on appropriate local elliptic Calabi-Yau manifolds engineer six dimensional superconformal field theories and their mass deformations. The partition function $Z_{top}$ of the refined topological string on these…

We investigate the structure of $\tau$-functions for the elliptic difference Painlev\'e equation of type $E_8$. Introducing the notion of ORG $\tau$-functions for the $E_8$ lattice, we construct some particular solutions which are expressed…

We study the regular surface defect in the Omega-deformed four-dimensional supersymmetric gauge theory with gauge group SU(N) with 2N hypermultiplets in fundamental representation. We prove its vacuum expectation value obeys the…

In their recent inspiring paper Mironov and Morozov claim a surprisingly simple expansion formula for the Kontsevich-Witten tau-function in terms of the Schur Q-functions. Here we provide a similar conjecture for the Br\'ezin-Gross-Witten…

We construct the gravity duals of large N supersymmetric gauge theories defined on squashed five-spheres with SU(3) x U(1) symmetry. These five-sphere backgrounds are continuously connected to the round sphere, and we find a one-parameter…

We describe a family of twisted partition functions for the relativistic spinning particle models. For suitable choices of fugacities this computes a refined Euler characteristics that counts the dimension of the physical states for…

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 propose an equivalence of the partition functions of two different 3d gauge theories. On one side of the correspondence we consider the partition function of 3d SL(2,R) Chern-Simons theory on a 3-manifold, obtained as a punctured Riemann…

In this paper we study several issues related to the generation of superpotential induced by background Ramond-Ramond fluxes in compactification of Type IIA string theory on Calabi-Yau four-folds. Identifying BPS solitons with D-branes…

We further explore the correspondence between N=2 supersymmetric SU(2) gauge theory with four flavors on epsilon-deformed backgrounds and conformal field theory, with an emphasis on the epsilon-expansion of the partition function natural…

In this paper we briefly review the main idea of the localization technique and its extension suitable in supersymmetric gauge field theory. We analyze the partition function of the vector multiplets with supercharges and its blocks on the…

We consider topological closed string theories on Calabi-Yau manifolds which compute superpotential terms in the corresponding compactified type II effective action. In particular, near certain singularities we compare the partition…

Surface operators in N=2 four-dimensional gauge theories are interesting half-BPS objects. These operators inherit the connection of gauge theory with the Liouville conformal field theory, which was discovered by Alday, Gaiotto and…

Let $\Omega$ be a flat torus and $G$ be the green's function of $-\Delta$ on $\Omega$. One intriguing mystery of $G$ is how the number of its critical points is related to blowup solutions of certain PDEs. In this article we prove that for…