F-theoretic vs microscopic description of a conformal N=2 SYM theory

TL;DR

This paper compares the F-theoretic and microscopic descriptions of a conformal N=2 SU(2) super Yang-Mills theory with four flavors, explicitly computing non-perturbative corrections and revealing a deep relation between four- and eight-dimensional dynamics.

Contribution

It provides an explicit non-perturbative computation of corrections in the D7/D3 system, confirming F-theoretic predictions and relating four-dimensional effective couplings to eight-dimensional quantum dynamics.

Findings

Non-perturbative corrections match F-theory predictions.

Effective coupling incorporates full quantum dynamics of an eight-dimensional scalar.

Relation between four-dimensional and eight-dimensional gauge theories established.

Abstract

The F-theory background of four D7 branes in a type I' orientifold was conjectured to be described by the Seiberg-Witten curve for the superconformal SU(2) gauge theory with four flavors. This relation was explained by considering in this background a probe D3 brane, which supports this theory with SU(2) realized as Sp(1). Here we explicitly compute the non-perturbative corrections to the D7/D3 system in type I' due to D-instantons. This computation provides both the quartic effective action on the D7 branes and the quadratic effective action on the D3 brane; the latter agrees with the F-theoretic prediction. The action obtained in this way is related to the one derived from the usual instanton calculus \`a la Nekrasov (or from its AGT realization in terms of Liouville conformal blocks) by means of a non-perturbative redefinition of the coupling constant. We also point out an intriguing relation between the four-dimensional theory on the probe D3 brane, which has a SO(8) flavor symmetry, and the eight-dimensional dynamics on the D7 branes. On the latter, SO(8) represents a gauge group and the flavor masses correspond to the vacuum expectation values of an adjoint scalar field m: what we find is that the exact effective coupling in four dimensions is obtained from its perturbative part by taking into account in its mass dependence the full quantum dynamics of the field m in eight dimensions.