Non‐perturbative gauge couplings from holography

Abstract

We show how D-instanton corrections modify the dilaton-axion profile emitted by an O7/D7 system turning it into the non-singular F-theory background which corresponds to the effective coupling on a D3 probe.

Non-perturbative gauge/gravity correspondence in $ \mathcal{N} $ = 2 theories

“…It is then natural to ask how the infinite tower of instanton effects is encoded in the holographic description of the gauge theory in terms of gravity. This question has been addressed recently in Ref.s [22]- [24], where a four-dimensional SU(2) gauge theory was matched to a background generated by a stack of D7 branes on top of an O7 orientifold plane. The dilaton-axion field governing the gauge coupling of the SU(2) theory was derived from disk amplitudes computing the emission from O7, D7 and D-instanton sources, and the result was expressed in terms of chiral correlators in the eight-dimensional gauge theory living on the D7/O7 system.…”

Non-perturbative aspects of gauge/gravity duality

“…Another possibility is to compute directly the multi-instanton corrections to the profiles of the gravitational bulk fields. This is what we will discuss in this contribution, which heavily relies on the content of [19,20,21] and especially of [22]. In particular we will briefly review how to derive the exact supergravity profile of the twisted field t emitted by a system of fractional D3-branes at a Z 2 -orbifold singularity supporting a N = 2 quiver gauge theory with unitary groups and bi-fundamental matter, and show how to obtain from it the exact running of the gauge coupling constant, including the non-perturbative contributions, in perfect agreement with…”

“…These correlators are in fact given by the integral 25) or alternatively, they can be obtained by expanding the generating functional [21] …”

“…In our brane set-up, instantons are introduced by adding fractional D(-1)-branes. Since we neglect the dynamics on the branes of type 1, we only [21,22]. Here we just recall that among the neutral moduli we have the bosonic and fermionic Goldstone modes of the supertranslations of the D3-brane world-volume which are broken by the D-instantons and which are identified with the superspace coordinates x and θ , and a complex scalar χ transforming in the adjoint representation of the instanton symmetry group U(k), whose eigenvalues describe the position of the D-instantons in the un-orbifolded directions transverse to the fractional D3-branes.…”

“…Here S inst (M k , Φ, T ) is the instanton action, describing the interactions of the instanton moduli with the boundary and bulk superfields. As explained in [21], such an action is…”