Related papers: Blowup Equations for Little Strings
We propose novel functional equations for the BPS partition functions of 6d (1,0) SCFTs, which can be regarded as an elliptic version of Gottsche-Nakajima-Yoshioka's K-theoretic blowup equations. From the viewpoint of geometric engineering,…
We generalize Nakajima-Yoshioka blowup equations to arbitrary gauge group with hypermultiplets in arbitrary representations. Using our blowup equations, we compute the instanton partition functions for 4d N=2 and 5d N=1 gauge theories for…
We establish the elliptic blowup equations for E-strings and M-strings and solve elliptic genera and refined BPS invariants from them. Such elliptic blowup equations can be derived from a path integral interpretation. We provide toric…
G\"{o}ttsche-Nakajima-Yoshioka K-theoretic blowup equations characterize the Nekrasov partition function of five dimensional $\mathcal{N}=1$ supersymmetric gauge theories compactified on a circle, which via geometric engineering correspond…
We propose a systematic approach to computing the BPS spectra of any 5d/6d supersymmetric quantum field theory in Coulomb phases, which admits either gauge theory descriptions or geometric descriptions, based on the Nakajima-Yoshioka's…
We study the elliptic genera of 6d strings based on their modular properties. They are weak Jacobi forms of weight 0, whose indices are determined from the 2d chiral anomalies. We propose the ansatz for the elliptic genera which reflects…
Given the recent geometrical classification of 6d $(1,0)$ SCFTs, a major question is how to compute for this large class their elliptic genera. The latter encode the refined BPS spectrum of the SCFTs, which determines geometric invariants…
The building blocks of 6d $(1,0)$ SCFTs include certain rank one theories with gauge group $G=SU(3),SO(8),F_4,E_{6,7,8}$. In this paper, we propose a universal recursion formula for the elliptic genera of all such theories. This formula is…
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 study twisted circle compactification of 6d $(2,0)$ SCFTs to 5d $\mathcal{N} = 2$ supersymmetric gauge theories with non-simply-laced gauge groups. We provide two complementary approaches towards the BPS partition functions, reflecting…
In this paper we develop a blow up analysis for solutions of a planar semilinear elliptic equation involving exponential nonlinearities. Such solutions describe cosmic strings, and we show how their blow up behaviour is characterised by new…
We give blow-up results for the Klein-Gordon equation and other perturbations of the semilinear wave equations with superlinear power nonlinearity, in one space dimension or in higher dimension under radial symmetry outside the origin.
Localization properties of fields in compact extra dimensions are crucial ingredients for string model building, particularly in the framework of orbifold compactifications. Realistic models often require a slight deviation from the…
We provide an efficient method of blowing up to compute leading order contributions of the recently introduced stringy canonical forms. The method is related to the well-known Hironaka's polyhedra game, and the given algorithm is also…
It is emphasized that compactified little string theories have compact moduli spaces of vacua, which globally probe compact string geometry. Compactifying various little string theories on T^3 leads to 3d theories with exact, quantum…
Compactification of the heterotic string on toroidal orbifolds is a promising set-up for the construction of realistic unified models of particle physics. The target space dynamics of such models, however, drives them slightly away from the…
In this paper, we consider blow-up behavior of weak solutions to a weakly coupled system for a semilinear damped wave equation and a semilinear wave equation in $\mathbb{R}^n$. This problem is part of the so-called Nakao's problem proposed…
We produce a finite time blow-up solution for nonlinear fractional heat equation ($\partial_t u + (-\Delta)^{\beta/2}u=u^k$) in modulation and Fourier amalgam spaces on the torus $\mathbb T^d$ and the Euclidean space $\mathbb R^d.$ This…
We apply the modular approach to computing the topological string partition function on non-compact elliptically fibered Calabi-Yau 3-folds with higher Kodaira singularities in the fiber. The approach consists in making an ansatz for the…
We give a sufficient condition for blow up of positive mild solutions to an initial value problem for a nonautonomous weakly coupled system with distinct fractional diffusions. The proof is based on the study of blow up of a particular…