Spectral curves of N $$ \mathcal{N} $$ = 1 theories of class S k $$ {\mathcal{S}}_k $$

String Webs and Curves of Marginal Stability in Five - Dimensional E N theories on S 1

We study curves of marginal stability (CMS) in five-dimensional N = 1 EN theories compactified on a circle using the D3-brane probe realization. In this realization, BPS states correspond to string webs in the affine EN 7-brane background and junction positions of the webs determine CMS. We find that there exist string webs involving infinitely many junctions. Consequently the EN theories have ...

On the Rational Recursive Sequence X_{N+1}=ƔX_{N-K}+(AX_N+BX_{N-K})⁄(CX_N-DX_{N-K})

Higgs branch localization of N = 1 theories on S 3 × S 1

We apply the method of Higgs branch localization to the N = 1 supersymmetric partition function on S3 × S1. As a result, we show that it can be written as the product of an elliptic vortex and anti-vortex partition function summed over a finite number of Higgs vacua.

Dynamics of higher order rational difference equation $x_{n+1}=(alpha+beta x_{n})/(A + Bx_{n}+ Cx_{n-k})$

The main goal of this paper is to investigate the periodic character, invariant intervals, oscillation and global stability and other new results of all positive solutions of the equation$$x_{n+1}=frac{alpha+beta x_{n}}{A + Bx_{n}+ Cx_{n-k}},~~ n=0,1,2,ldots,$$where the parameters $alpha$, $beta$, $A$, $B$ and $C$ are positive, and the initial conditions $x_{-k},x_{-k+1},ldots,x_{-1},x_{0}$ are...

String Webs and Curves of Marginal Stability in Five - Dimensional E N theories on S 1 Yukiko Ohtake

We study curves of marginal stability (CMS) in five-dimensional N = 1 EN theories compactified on a circle using the D3-brane probe realization. In this realization, BPS states correspond to string webs in the affine EN 7-brane background and junction positions of the webs determine CMS. We find that there exist string webs involving infinitely many junctions. Consequently the EN theories have ...