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Giancarlo Rossi

Publications and source records attributed to Giancarlo Rossi.

48 records · Page 3Linked to original sources
arXiv2003

Surprises from the Resolution of Operator Mixing in N = 4 SYM

We reexamine the problem of operator mixing in N = 4 SYM. Particular attention is paid to the correct definition of composite gauge invariant local operators, which is necessary for the computation of their anomalous dimensions beyond lowest order. As an application we reconsider the case of operators with naive dimension Delta_0=4, already studied in the literature. Stringent constraints from the resummation of logarithms in power behaviours are exploited and the role of the generalized N = 4 Konishi anomaly in the mixing with operators involving fermions is discussed. A general method for the explicit (numerical) resolution of the operator mixing and the computation of anomalous dimensions is proposed. We then resolve the order g^2 mixing for the 15 (purely scalar) singlet operators of naive dimension Δ_0=6. Rather surprisingly we find one isolated operator which has a vanishing anomalous dimension up to order g^4, belonging to an apparently long multiplet. We also solve the order g^2 mixing for the 26 operators belonging to the representation 20' of SU(4). We find an operator with the same one-loop anomalous dimension as the Konishi multiplet.

hep-th↗
arXiv2002

On Operator Mixing in N=4 SYM

We resolve the mixing of the scalar operators of naive dimension 4 belonging to the representation 20' of the SU(4) R-symmetry in N=4 SYM. We compute the order g^2 corrections to their anomalous dimensions and show the absence of instantonic contributions thereof. Ratios of the resulting expressions are irrational numbers, even in the large N limit where, however, we observe the expected decoupling of double-trace operators from single-trace ones. We briefly comment on the generalizations of our results required in order to make contact with the double scaling limit of the theory conjectured to be holographically dual to type IIB superstring on a pp-wave.

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arXiv2001

Properties of the Konishi multiplet in N=4 SYM theory

We study perturbative and non-perturbative properties of the Konishi multiplet in N=4 SYM theory in D=4 dimensions. We compute two-, three- and four-point Green functions with single and multiple insertions of the lowest component of the multiplet, and of the lowest component of the supercurrent multiplet. These computations require a proper definition of the renormalized operator and lead to an independent derivation of its anomalous dimension. The O(g^2) value found in this way is in agreement with previous results. We also find that instanton contributions to the above correlators vanish. From our results we are able to identify some of the lowest dimensional gauge-invariant composite operators contributing to the OPE of the correlation functions we have computed. We thus confirm the existence of an operator belonging to the representation 20', which has vanishing anomalous dimension at order g^2 and g^4 in perturbation theory as well as at the non-perturbative level, despite the fact that it does not obey any of the known shortening conditions.

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arXiv1999

Lattice QCD, O.P.E. and the Standard Model

A number of old and new methods for computing $K\toππ$ amplitudes on the lattice are reevaluated. They all involve a non-perturbative determination of matching coefficients. I will show how problems related to operator mixing can be greatly reduced by introducing the O.P.E. of hadronic currents directly on the lattice. Applications to the evaluation of CP-symmetric ($ΔI = 1/2$ rule) and CP-violating ($ε'/ε$) processes are presented.

hep-lat↗
arXiv1999

On the logarithmic behaviour in N=4 SYM theory

We show that the logarithmic behaviour seen in perturbative and non perturbative contributions to Green functions of gauge-invariant composite operators in N=4 SYM with SU(N) gauge group can be consistently interpreted in terms of anomalous dimensions of unprotected operators in long multiplets of the superconformal group SU(2,2|4). In order to illustrate the point we analyse the short-distance behaviour of a particularly simple four-point Green function of the lowest scalar components of the N=4 supercurrent multiplet. Assuming the validity of the Operator Product Expansion, we are able to reproduce the known value of the one-loop anomalous dimension of the single-trace operators in the Konishi supermultiplet. We also show that it does not receive any non-perturbative contribution from the one-instanton sector. We briefly comment on double- and multi-trace operators and on the bearing of our results on the AdS/SCFT correspondence.

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arXiv1998

Instantons in supersymmetric Yang-Mills and D-instantons in IIB superstring theory

The one-instanton contributions to various correlation functions of supercurrents in four-dimensional N=4 supersymmetric SU(2) Yang-Mills theory are evaluated to the lowest order in perturbation theory.Expressions of the same form are obtained from the leading effects of a single D-instanton extracted from the IIB superstring effective action around the AdS5*S5 background. This is in line with the suggested AdS/Yang-Mills correspondence. The relation between Yang--Mills instantons and D-instantons is further confirmed by the explicit form of the classical D-instanton solution in the AdS5*S5 background and its associated supermultiplet of zero modes. Speculations are made concerning instanton effects in the large-N_c limit of the SU(N_c) Yang-Mills theory.

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arXiv1996

DIS Structure Functions in Lattice QCD

In this talk I present the complete 1-loop perturbative computation of the renormalization constants and mixing coefficients of quark and gluon lattice operators of rank two and three whose hadronic elements enter in the determination of the first and second moment of Deep Inelastic Scattering Structure Functions, making use of the nearest-neighbor improved ``clover-leaf'' lattice QCD action. To perform the huge amount of calculations required for the evaluation of all the relevant Feynman diagrams, extensive use of symbolic manipulation languages like Schoonschip and Form has been made.

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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↗
arXiv1995

Deep Inelastic Scattering in Improved Lattice QCD. II. The second moment of structure functions

In this paper we present the 1-loop perturbative computation of the renormalization constants and mixing coefficients of the lattice quark operators of rank three whose hadronic elements enter in the determination of the second moment of Deep Inelastic Scattering (DIS) structure functions. We have employed in our calculations the nearest-neighbor improved ``clover-leaf'' lattice QCD action. The interest of using this action in Monte Carlo simulations lies in the fact that all terms which in the continuum limit are effectively of order $a$ ($a$ being the lattice spacing) have been demonstrated to be absent from on-shell hadronic lattice matrix elements. We have limited our computations to the quenched case, in which quark operators do not mix with gluon operators. We have studied the transformation properties under the hypercubic group of the operators up to the rank five (which are related to moments up to the fourth of DIS structure functions), and we discuss the choice of the operators considered in this paper together with the feasibility of lattice computations for operators of higher ranks. To perform the huge amount of calculations required for the evaluation of all the relevant Feynman diagrams, we have extensively used the symbolic manipulation languages Schoonschip and Form.

hep-lat↗
arXiv1995

The Use of Schoonschip and Form in Perturbative Lattice Calculations

Using the formal languages Schoonschip and Form, we have developed general codes that are able to carry out all the algebraic manipulations needed to perform analytic lattice calculations, starting from the elementary building blocks (propagators and vertices) of each Feynman diagram. The main difficulty resides in the fact that, although there are many built in instructions to deal with Dirac gamma-matrices, Schoonschip and Form have been conceived having in mind a continuum theory, which is invariant with respect to the Lorentz group. On the lattice, on the contrary, a field theory is only invariant with respect to the hypercubic group, contained in the (euclidean) Lorentz group and not every pair of equal indices should be summed over. Being impossible to directly use the `gammatrics' of Schoonschip and Form as they are, special routines have been developed to correctly treat gamma matrices on the lattice, while using as much as possible of the built in Schoonschip and Form commands. We have used our codes to compute, in 1-loop perturbation theory in lattice QCD, the renormalization constants and mixing coefficients of the operators that enter in the determination of the first two moments of deep inelastic scattering structure functions.

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arXiv1994

Deep Inelastic Scattering in Improved Lattice QCD. I. The first moment of structure functions

We present the complete 1-loop perturbative computation of the renormalization constants and mixing coefficients of the operators that measure the first moment of deep inelastic scattering structure functions, employing the nearest neighbor improved lattice QCD action. The interest of using this action in Monte Carlo simulations lies in the fact that all terms which in the continuum limit are effectively of order $a$ ($a$ being the lattice spacing) have been proven to be absent from on-shell hadronic lattice matrix elements. Because of the complexity of the calculations, we have checked the analytical expression of all Feynman diagrams using Schoonschip. To this end we have developed a suitable code designed to automatically carry out all the necessary lattice algebraic manipulations, starting from the elementary building blocks of each diagram. We have found discrepancies with some of the published numbers, but we are in agreement with the known results on the energy-momentum tensor.

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