Towards superconformal and quasi-modular representation of exotic smooth R^4 from superstring theory II

TL;DR

This paper explores how exotic smooth structures on R^4 relate to superstring theory, quasi-modular forms, and Seiberg-Witten theory, revealing new connections between geometry, supersymmetry, and quantum field theories.

Contribution

It demonstrates the emergence of quasi-modular forms from exotic R^4 structures and links string theory correlation functions to Seiberg-Witten prepotentials in a novel geometric context.

Findings

Quasi-modular forms arise from exotic R^4 structures.

String theory correlation functions generate Seiberg-Witten prepotentials.

Exotic R^4 spaces connect supersymmetric and non-supersymmetric Yang-Mills theories.

Abstract

This is the second part of the work where quasi-modular forms emerge from small exotic smooth $\mathbb{R}^4$'s grouped in a fixed radial family. SU(2) Seiberg-Witten theory when formulated on exotic $\mathbb{R}^4$ from the radial family, in special foliated topological limit can be described as SU(2) Seiberg-Witten theory on flat standard $\mathbb{R}^4$ with the gravitational corrections derived from coupling to ${\cal N}=2$ supergravity. Formally, quasi-modular expressions which follow the Connes-Moscovici construction of the universal Godbillon-Vey class of the codimension-1 foliation, are related to topological correlation functions of superstring theory compactified on special Callabi-Yau manifolds. These string correlation functions, in turn, generate Seiberg-Witten prepotential and the couplings of Seiberg-Witten theory to ${\cal N}=2$ supergravity sector. Exotic 4-spaces are conjectured to serve as a link between supersymmetric and non-supersymmetric Yang-Mills theories in dimension 4.