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A. Santambrogio

Publications and source records attributed to A. Santambrogio.

16 recordsLinked to original sources
arXiv2010

Superspace calculation of the four-loop spectrum in N=6 supersymmetric Chern-Simons theories

Using N=2 superspace techniques we compute the four-loop spectrum of single trace operators in the SU(2) x SU(2) sector of ABJM and ABJ supersymmetric Chern-Simons theories. Our computation yields a four-loop contribution to the function h^2(λ) (and its ABJ generalization) in the magnon dispersion relation which has fixed maximum transcendentality and coincides with the findings in components given in the revised versions of arXiv:0908.2463 and arXiv:0912.3460. We also discuss possible scenarios for an all-loop function h^2(λ) that interpolates between weak and strong couplings.

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arXiv2008

Wrapping at four loops in N=4 SYM

We present the planar four-loop anomalous dimension of the composite operator tr(phi[Z,phi]Z) in the flavour SU(2) sector of the N=4 SYM theory. At this loop order wrapping interactions are present: they give rise to contributions proportional to zeta(5) increasing the level of transcendentality of the anomalous dimension. In a sequel of this paper all the details of our calculation will be reported.

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arXiv2008

Finite-size effects in the superconformal beta-deformed N=4 SYM

We study finite size effects for composite operators in the SU(2) sector of the superconformal beta-deformed N=4 SYM theory. In particular we concentrate on the spectrum of one single magnon. Since in this theory one-impurity states are non BPS we compute their anomalous dimensions including wrapping contributions up to four loops and discuss higher order effects.

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arXiv2008

Anomalous dimension with wrapping at four loops in N=4 SYM

In this paper we give all the details of the calculation that we presented in our previous paper arXiv:0712.3522, concerning the four-loop anomalous dimension of the Konishi descendant tr(ϕZϕZ-ϕϕZ Z) in the SU(2) sector of the N=4 planar SYM theory. We explicitly consider all the wrapping diagrams that we compute using an N=1 superspace approach and Gegenbauer polynomial x-space techniques.

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arXiv2003

Four-point correlators of BPS operators in N=4 SYM at order g^4

We study the large N degeneracy in the structure of the four-point amplitudes of 1/2-BPS operators of arbitrary weight k in perturbative N=4 SYM theory. At one loop (order g^2) this degeneracy manifests itself in a smaller number of independent conformal invariant functions describing the amplitude, compared to AdS_5 supergravity results. To study this phenomenon at the two-loop level (order g^4) we consider a particular N=2 hypermultiplet projection of the general N=4 amplitude. Using the formalism of N=2 harmonic superspace we then explicitly compute this four-point correlator at two loops and identify the corresponding conformal invariant functions. In the cases of 1/2-BPS operators of weight k=3 and k=4 the one-loop large N degeneracy is lifted by the two-loop corrections. However, for weight k > 4 the degeneracy is still there at the two-loop level. This behavior suggests that for a given weight k the degeneracy will be removed if perturbative corrections of sufficiently high order are taken into account. These results are in accord with the AdS/CFT duality conjecture.

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arXiv2002

Non-protected operators in N=4 SYM and multiparticle states of AdS_5 SUGRA

We study a class of non-protected local composite operators which occur in the R symmetry singlet channel of the OPE of two stress-tensor multiplets in {\cal N}=4 SYM. At tree level these are quadrilinear scalar dimension four operators, two single-traces and two double-traces. In the presence of interaction, due to a non-trivial mixing under renormalization, they split into linear combinations of conformally covariant operators. We resolve the mixing by computing the one-loop two-point functions of all the operators in an {\cal N}=1 setup, then diagonalizing the anomalous dimension matrix and identifying the quasiprimary operators. We find one operator whose anomalous dimension is negative and suppressed by a factor of 1/N^2 with respect to the anomalous dimensions of the Konishi-like operators. We reveal the mechanism responsible for this suppression and argue that it works at every order in perturbation theory. In the context of the AdS/CFT correspondence such an operator should be dual to a multiparticle supergravity state whose energy is less than the sum of the corresponding individual single-particle states.

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arXiv2002

Nonabelian Born-Infeld from Super-Yang-Mills effective action

We discuss recent results on one-loop contributions to the effective action in {\cal N}=4 supersymmetric Yang-Mills theory in four dimensions. Contributions with five external vector fields are compared with corresponding ones in open superstring theory in order to understand the relation with the F^5 terms that appear in the nonabelian generalization of the Born-Infeld action.

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arXiv2000

More on correlators and contact terms in {\cal N}=4 SYM at order g^4

We compute two-point functions of chiral operators Tr(Φ^k) for any k, in {\cal N}=4 supersymmetric SU(N) Yang-Mills theory. We find that up to the order g^4 the perturbative corrections to the correlators vanish for all N. The cancellation occurs in a highly non trivial way, due to a complicated interplay between planar and non planar diagrams. In complete generality we show that this same result is valid for any simple gauge group. Contact term contributions signal the presence of ultraviolet divergences. They are arbitrary at the tree level, but the absence of perturbative renormalization in the non singular part of the correlators allows to compute them unambiguously at higher orders. In the spirit of the AdS/CFT correspondence we comment on their relation to infrared singularities in the supergravity sector.

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arXiv2000

Embedding Branes in Flat Two-time Spaces

We show how non-near horizon, non-dilatonic $p$-brane theories can be obtained from two embedding constraints in a flat higher dimensional space with 2 time directions. In particular this includes the construction of D3 branes from a flat 12-dimensional action, and M2 and M5 branes from 13 dimensions. The worldvolume actions are found in terms of fields defined in the embedding space, with the constraints enforced by Lagrange multipliers.

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arXiv1999

$(α')^4$ corrections to the N=2 supersymmetric Born-Infeld action

We consider the N=2 supersymmetric Born-Infeld action and compute one-loop divergences quantizing the theory in N=1 superspace. We find that in the presence of non constant curvature the theory is not renormalizable. The structure of the $(α')^4$ counterterm, proportional to derivatives of the curvature, is consistent with effective action calculations from superstring theory.

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arXiv1999

Two-point functions of chiral operators in {\cal N}=4 SYM at order g^4

We compute two-point functions of chiral operators Tr Φ^3 in {\cal N}=4 SU(N) supersymmetric Yang-Mills theory to the order g^4 in perturbation theory. We perform explicit calculations using {\cal N}=1 superspace techniques and find that perturbative corrections to the correlators vanish for all N. While at order g^2 the cancellations can be ascribed to the nonrenormalization theorem valid for correlators of operators in the same multiplet as the stress tensor, at order g^4 this argument no longer applies and the actual cancellation occurs in a highly nontrivial way. Our result is obtained in complete generality, without the need of additional conjectures or assumptions. It gives further support to the belief that such correlators are not renormalized to all orders in g and to all orders in N.

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arXiv1998

Non-transversal colliding singularities in F-theory

This is a short introduction to the study of compactifications of F-theory on elliptic Calabi-Yau threefolds near colliding singularities. In particular we consider the case of non-transversal intersections of the singular fibers.

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arXiv1997

Gravitational Dressing of N=2 Sigma-Models Beyond Leading Order

We study the beta-function of the N=2 sigma-model coupled to N=2 induced supergravity. We compute corrections to first order in the semiclassical limit, $c \to -\infty$, beyond one-loop in the matter fields. As compared to the corresponding bosonic, metric sigma-model calculation, we find new types of contributions arising from the dilaton coupling automatically accounted for, once the Kähler potential is coupled to N=2 supergravity.

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arXiv1996

Quantizing N=2 matter-supergravity systems

We consider $N=2$ supergravity coupled to $N=2$ Yang--Mills matter and discuss the nature of one--loop divergences. Using $N=1$ superfields and superspace methods, we describe the quantization of the system in the abelian case.

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arXiv1996

Renormalization Group Flows in Sigma--Models Coupled to Two--Dimensional Dynamical Gravity

We consider a bosonic $\s$--model coupled to two--dimensional gravity. In the semiclassical limit, $c\rightarrow -\infty$, we compute the gravity dressing of the $\b$--functions at two--loop order in the matter fields. We find that the corrections due to the presence of dynamical gravity are {\em not} expressible simply in terms of a multiplicative factor as previously obtained at the one--loop level. Our result indicates that the critical points of the theory are nontrivially influenced and modified by the induced gravity.

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