The M5-brane on K3 and del Pezzo's and multi-loop string amplitudes

TL;DR

This paper explores the BPS spectrum of Little String Theory with M5-branes on complex manifolds, revealing multi-loop string amplitude structures and novel theta-function appearances linked to dualities in string and gauge theories.

Contribution

It uncovers the reconstruction of heterotic contributions in M-theory compactifications and identifies theta-functions arising from wrapped M5-branes on del Pezzo surfaces, connecting SYM theories and CFTs.

Findings

Reconstruction of g-loop heterotic contributions in M-theory.

Emergence of theta-functions from wrapped M5-branes on del Pezzo surfaces.

Links between 4D SYM theories and 2D CFTs via dualities.

Abstract

We study the BPS spectrum of Little String Theory for bound states of M5-branes wrapped on six manifold of product topology $M_4\times\Sigma_2$ and the apparence of multi-loop $\theta$-functions in a supersymmetric index calculation. We find a total reconstruction of the g-loop heterotic contribution in the case of a double K3 M-theory compactification. Moreover, we consider total wrapping of M5-branes on del Pezzo surfaces $B_k$ and, by studying the relevant amplitude, we notice the arising of $\theta$-functions relative to BPS strings on $T^{k-1}$, i.e. membranes on $T^k$. This happens because of beautiful relations between four dimensional SYM theories and CFTs in two dimensions and seems to be linked to a duality recently observed by A.Iqbal, A.Neitzke and C.Vafa in.