Alessandro Tanzini

Multi-Instanton Calculus and Equivariant Cohomology

We present a systematic derivation of multi-instanton amplitudes in terms of ADHM equivariant cohomology. The results rely on a supersymmetric formulation of the localization formula for equivariant forms. We examine the cases of N = 4 and N = 2 gauge theories with adjoint and fundamental matter.

A note on string interaction on the pp-wave background

We consider type IIB string interaction on the maximally supersymmetric pp-wave background and discuss how the bosonic symmetries of the background are realized. This analysis shows that there are some interesting differences with respect to the flat-space case and suggests modifications to the existing form of the string vertex. We focus on the zero-mode part which is responsible for some puzzling string predictions about the super Yang–Mills side. We show that these puzzles disappear when a symmetry preserving string interaction is used.

String interactions and discrete symmetries of the pp-wave background

Free string theory on the plane-wave background displays a discrete Z2 symmetry exchanging the two transverse SO(4) rotation groups. This symmetry should be respected also at the interacting level. We show that the zero-mode structure proposed in Chu et al (2002 Preprint hep-th/0208148) can be completed to a full kinematical vertex, contrary to claims appearing in the previous literature. We also comment on the relation with recent works on the string-bit formalism and on the comparison with the field theory side of the correspondence.

N=2 Super Yang–Mills and the XXZ spin chain

Abstract We analyse the renormalisation properties of composite operators of scalar fields in the N = 2 Super Yang–Mills theory. We compute the matrix of anomalous dimensions in the planar limit at one-loop order in the ’t Hooft coupling, and show that it corresponds to the Hamiltonian of an integrable XXZ spin chain with an anisotropy parameter Δ > 1 . We suggest that this parameter could be related to the presence of non-trivial two-form fluxes in the dual supergravity background. We find that the running of the gauge coupling does not affect the renormalisation group equations for these composite operators at one-loop order, and argue that this is a general property of gauge theories which is not related to supersymmetry.

D-instanton probes of non-conformal geometries

D-instanton calculus has proved to be able to probe the AdS near horizon geometry for N D-branes systems which, when decoupled from gravity, yield four-dimensional superconformal gauge theories with various matter content. In this work we extend previous analysis to encompass fractional brane models which give rise to non-conformal = 2 Super Yang-Mills theories. Via D-instanton calculus we study the geometry of such models for finite N and recover the β function of the gauge coupling constants which is expected in non-conformal gauge theories. We also give a topological matrix theory formulation for the D-instanton action of these theories. Finally, we revisit the related system where the D3-branes wrap a 4/p orbifold singularity and the D(-1)-branes are associated to instanton solutions of four-dimensional gauge theories in the blown down ALE space.

D-instantons on orbifolds and gauge/gravity correspondence

D-instantons are used to probe the near-horizon geometry of D3-branes systems on orbifold spaces. For fractional D3-branes, D-instanton calculus correctly reproduces the gauge β-function and U(1)R anomaly of the corresponding = 2 non-conformal Super Yang-Mills theories. For D3-branes wrapping the orbifold singularity, D-instantons can be identi.ed with gauge instantons on ALE space, providing evidence of AdS/CFT duality for gauge theories on curved spaces.