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Francesco Fucito

Publications and source records attributed to Francesco Fucito.

45 records · Page 3Linked to original sources
arXiv2001

D-instanton probes of N=2 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 N=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 ${\real}^4/{\zet}_p$ orbifold singularity and the D(-1) branes are associated to instanton solutions of four-dimensional gauge theories in the blown down ALE space.

hep-th↗
arXiv2000

On the Multi-Instanton Measure for Super Yang--Mills Theories

In this paper we revisit the arguments that have led to the proposal of a multi-instanton measure for supersymmetric Yang-Mills theories. We then recall how the moduli space of gauge connections on $\real^4$ can be built from a hyperkähler quotient construction which we generalize to supermanifolds. The measure we are looking for is given by the supermetric of the supermoduli space thus introduced. To elucidate the construction we carry out explicit computations in the case of N=2 supersymmetric Yang-Mills theories.

hep-th↗
arXiv2000

Instanton Calculus, Topological Field Theories and N=2 Super Yang-Mills Theories

The results obtained by Seiberg and Witten for the low-energy Wilsonian effective actions of N=2 supersymmetric theories with gauge group SU(2) are in agreement with instanton computations carried out for winding numbers one and two. This suggests that the instanton saddle point saturates the non-perturbative contribution to the functional integral. A natural framework in which corrections to this approximation are absent is given by the topological field theory built out of the N=2 Super Yang-Mills theory. After extending the standard construction of the Topological Yang-Mills theory to encompass the case of a non-vanishing vacuum expectation value for the scalar field, a BRST transformation is defined (as a supersymmetry plus a gauge variation), which on the instanton moduli space is the exterior derivative. The topological field theory approach makes the so-called "constrained instanton" configurations and the instanton measure arise in a natural way. As a consequence, instanton-dominated Green's functions in N=2 Super Yang-Mills can be equivalently computed either using the constrained instanton method or making reference to the topological twisted version of the theory. We explicitly compute the instanton measure and the contribution to $u=<\Tr ϕ^2>$ for winding numbers one and two. We then show that each non-perturbative contribution to the N=2 low-energy effective action can be written as the integral of a total derivative of a function of the instanton moduli. Only instanton configurations of zero conformal size contribute to this result. Finally, the 8k-dimensional instanton moduli space is built using the hyperkahler quotient procedure, which clarifies the geometrical meaning of our approach.

hep-th↗
arXiv1998

Gauge Zero-Modes on ALE Manifolds

In this paper we find the general (i.e. valid for arbitrary values of the winding number) form of the gauge zero-modes, in the adjoint representation, for theories living on manifolds of the ALE type.

hep-th↗
arXiv1997

Non-holomorphic terms in N=2 SUSY Wilsonian actions and RG equation

In this paper we first investigate the Ansatz of one of the present authors for K(Ψ,\barΨ), the adimensional modular invariant non-holomorphic correction to the Wilsonian effective Lagrangian of an N=2 globally supersymmetric gauge theory. The renormalisation group beta-function of the theory crucially allows us to express K(Ψ,\barΨ) in a form that easily generalises to the case in which the theory is coupled to N_F hypermultiplets in the fundamental representation of the gauge group. This function satisfies an equation which should be viewed as a fully non-perturbative ``non-chiral superconformal Ward identity". We also determine its renormalisation group equation. Furthermore, as a first step towards checking the validity of this Ansatz, we compute the contribution to K(Ψ,\barΨ) from instantons of winding number k=1 and k=2. As a by-product of our analysis we check a non-renormalisation theorem for N_F=4.

hep-th↗
arXiv1996

A New Nonperturbative Approach to QCD by BF Theory

Yang-Mills theory in the first order formalism appears as the deformation of a topological field theory, the pure BF theory. In this approach new non local observables are inherited from the topological theory and the operators entering the t'Hooft algebra find an explicit realization. A calculation of the {\it vev}'s of these operators is performed in the Abelian Projection gauge.

hep-th↗
arXiv1996

Instanton Calculus and Nonperturbative Relations in N=2 Supersymmetric Gauge Theories

Using instanton calculus we check, in the weak coupling region, the nonperturbative relation $$ <\Trϕ^2>=iπ\left(\cf-{a\over 2} {\partial\cf\over\partial a}\right)$$ obtained for a N=2 globally supersymmetric gauge theory. Our computations are performed for instantons of winding number k, up to k=2 and turn out to agree with previous nonperturbative results.

hep-th↗
arXiv1996

Explicit Construction of Yang-Mills Instantons on ALE Spaces

We describe the explicit construction of Yang-Mills instantons on ALE spaces, following the work of Kronheimer and Nakajima. For multicenter ALE metrics, we determine the abelian instanton connections which are needed for the construction in the non-abelian case. We compute the partition function of Maxwell theories on ALE manifolds and comment on the issue of electromagnetic duality. We discuss the topological characterization of the instanton bundles as well as the identification of their moduli spaces. We generalize the 't Hooft ansatz to SU(2) instantons on ALE spaces and on other hyper-Kahler manifolds. Specializing to the Eguchi-Hanson gravitational background, we explicitly solve the ADHM equations for SU(2) gauge bundles with second Chern class 1/2, 1 and 3/2.

hep-th↗