arXiv subjects

M. Bochicchio

Publications and source records attributed to M. Bochicchio.

3 recordsLinked to original sources

arXiv2024

Generating functional of correlators of twist-$2$ operators in $\mathcal{N} = 1$ SUSY Yang-Mills theory, II

This article represents the second installment, in which we calculate the generating functional of correlators of collinear twist-$2$ operators that are components of unbalanced superfields-i.e., superfields possessing an unequal number of dotted and undotted indices in their spinor representation-in $\mathcal{N} = 1$ SUSY SU($N$) YM theory. The analysis is performed in both Minkowskian and Euclidean space-time, in the conformal limit and its renormalization-group (RG) improved form to the leading and next-to-leading order of the large-$N$ expansion. The corresponding generating functional for correlators of balanced superfields was addressed in the first installment of this work. Finally, we compare our asymptotic RG-improved generating functional at the next-to-leading large-$N$ order with the corresponding nonperturbative object that originates from the glueball/gluinoball one-loop effective action, to which it should be asymptotic at short distances due to asymptotic freedom. It is noteworthy that we discover both objects share the structure of the logarithm of a functional superdeterminant. Consequently, our large-$N$ calculation imposes stringent ultraviolet asymptotic constraints on the nonperturbative solution of large-$N$ $\mathcal{N} = 1$ SUSY YM theory, which could serve as a crucial guide in the quest for such a solution.

hep-th↗

arXiv2013

Ultraviolet asymptotics of glueball propagators

We point out that perturbation theory in conjunction with the renormalization group (RG) puts a severe constraint on the structure of the large-N non-perturbative glueball propagators in SU(N) pure YM, in QCD and in n=1 SUSY QCD with massless quarks, or in any confining asymptotically-free gauge theory massless in perturbation theory. For the scalar and pseudoscalar glueball propagators in pure YM and QCD with massless quarks we check in detail the RG-improved estimate to the order of the leading and next-to-leading logarithms by means of a remarkable three-loop computation by Chetyrkin et al. We investigate as to whether the aforementioned constraint is satisfied by any of the scalar or pseudoscalar glueball propagators computed in the framework of the AdS String/ large-N Gauge Theory correspondence and of a recent proposal based on a Topological Field Theory underlying the large-N limit of YM. We find that none of the proposals for the scalar or the pseudoscalar glueball propagators based on the AdS String/ large-N Gauge Theory correspondence satisfies the constraint, actually as expected, since the gravity side of the correspondence is in fact strongly coupled in the ultraviolet. On the contrary, the Topological Field Theory satisfies the constraint that follows by the asymptotic freedom.

hep-th↗

arXiv2013

Gauge theories in anti-selfdual variables

Some years ago the Nicolai map, viewed as a change of variables from the gauge connection in a fixed gauge to the anti-selfdual part of the curvature, has been extended by the first named author to pure YM from its original definition in N=1 SUSY YM. We study here the perturbative 1PI effective action in the anti-selfdual variables of any gauge theory, in particular pure YM, QCD and N=1 SUSY YM. We prove that the one-loop 1PI effective action of a gauge theory mapped to the anti-selfdual variables in any gauge is identical to the one of the original theory. This is due to the conspiracy between the Jacobian of the change to the anti-selfdual variables and an extra functional determinant that arises from the non-linearity of the coupling of the anti-selfdual curvature to an external source in the Legendre transform that defines the 1PI effective action. Hence we establish the one-loop perturbative equivalence of the mapped and original theories on the basis of the identity of the one-loop 1PI effective actions. Besides, we argue that the identity of the perturbative 1PI effective actions extends order by order in perturbation theory.

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