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Silvia Penati

Publications and source records attributed to Silvia Penati.

At least 73 records · Page 4Linked to original sources
arXiv2006

Non(anti)commutative SYM theory: Renormalization in superspace

We present a systematic investigation of one-loop renormalizability for nonanticommutative N=1/2, U(N) SYM theory in superspace. We first discuss classical gauge invariance of the pure gauge theory and show that in contradistinction to the ordinary anticommutative case, different representations of supercovariant derivatives and field strengths do not lead to equivalent descriptions of the theory. Subsequently we develop background field methods which allow us to compute a manifestly covariant gauge effective action. One-loop evaluation of divergent contributions reveals that the theory simply obtained from the ordinary one by trading products for star products is not renormalizable. In the case of SYM with no matter we present a N=1/2 improved action which we show to be one-loop renormalizable and which is perfectly compatible with the algebraic structure of the star product. For this action we compute the beta functions. A brief discussion on the inclusion of chiral matter is also presented.

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arXiv2005

Exact results in planar N=1 superconformal Yang-Mills theory

In the β-deformed N=4 supersymmetric SU(N) Yang-Mills theory we study the class of operators O_J = Tr(Φ_i^J Φ_k), i\neq k and compute their exact anomalous dimensions for N,J\to\infty. This leads to a prediction for the masses of the corresponding states in the dual string theory sector. We test the exact formula perturbatively up to two loops. The consistency of the perturbative calculation with the exact result indicates that in the planar limit the one--loop condition g^2=h\bar{h} for superconformal invariance is indeed sufficient to insure the {\em exact} superconformal invariance of the theory. We present a direct proof of this point in perturbation theory. The O_J sector of this theory shares many similarities with the BMN sector of the N=4 theory in the large R--charge limit.

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arXiv2005

Two-point correlators in the beta-deformed N=4 SYM at the next-to-leading order

We compute two-point functions of lowest weight operators at the next-to-leading order in the couplings for the beta-deformed N=4 SYM. In particular we focus on the CPO Tr(Phi_1^2) and the operator Tr(Phi_1 Phi_2) not presently listed as BPS. We find that for both operators no anomalous dimension is generated at this order, then confirming the results recently obtained in hep-th/0506128. However, in both cases a finite correction to the two-point function appears.

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arXiv2004

Some properties of the integrable noncommutative sine-Gordon system

In this paper we continue the program, initiated in Ref. hep-th/0112246, to investigate an integrable noncommutative version of the sine-Gordon model. We discuss the origin of the extra constraint which the field function has to satisfy in order to guarantee classical integrability. We show that the system of constraint plus dynamical equation of motion can be obtained by a suitable reduction of a noncommutative version of 4d self-dual Yang-Mills theory. The field equations can be derived from an action which is the sum of two WZNW actions with cosine potentials corresponding to a complexified noncommutative U(1) gauge group. A brief discussion of the relation with the bosonized noncommutative Thirring model is given. In spite of integrability we show that the S-matrix is acasual and particle production takes place.

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arXiv2004

Integrable Noncommutative Sine-Gordon Model

Requiring an infinite number of conserved local charges or the existence of an underlying linear system does not uniquely determine the Moyal deformation of 1+1 dimensional integrable field theories. As an example, the sine-Gordon model may be obtained by dimensional and algebraic reduction from 2+2 dimensional self-dual U(2) Yang-Mills through a 2+1 dimensional integrable U(2) sigma model, with some freedom in the noncommutative extension of this algebraic reduction. Relaxing the latter from U(2)->U(1) to U(2)->U(1)xU(1), we arrive at novel noncommutative sine-Gordon equations for a pair of scalar fields. The dressing method is employed to construct its multi-soliton solutions. Finally, we evaluate various tree-level amplitudes to demonstrate that our model possesses a factorizable and causal S-matrix in spite of its time-space noncommutativity.

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arXiv2003

Two-loop Renormalization for Nonanticommutative N=1/2 Supersymmetric WZ Model

We study systematically, through two loops, the divergence structure of the supersymmetric WZ model defined on the N=1/2 nonanticommutative superspace. By introducing a spurion field to represent the supersymmetry breaking term F^3 we are able to perform our calculations using conventional supergraph techniques. Divergent terms proportional to F, F^2 and F^3 are produced (the first two are to be expected on general grounds) but no higher-point divergences are found. By adding ab initio F and F^2 terms to the original lagrangian we render the model renormalizable. We determine the renormalization constants and beta functions through two loops, thus making it possible to study the renormalization group flow of the nonanticommutation parameter.

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arXiv2003

Non(anti)commutative Superspace

We investigate the most general non(anti)commutative geometry in N=1 four-dimensional superspace, invariant under the classical (i.e., undeformed) supertranslation group. We find that a nontrivial non(anti)commutative superspace geometry compatible with supertranslations exists with non(anti)commutation parameters which may depend on the spinorial coordinates. The algebra is in general nonassociative. Imposing associativity introduces additional constraints which however allow for nontrivial commutation relations involving fermionic coordinates. We obtain explicitly the first three terms of a series expansion in the deformation parameter for a possible associative *-product. We also consider the case of N=2 euclidean superspace where the different conjugation relations among spinorial coordinates allow for a more general supergeometry.

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arXiv2002

An integrable noncommutative version of the sine--Gordon system

Using the bicomplex approach we discuss a noncommutative system in two--dimensional Euclidean space. It is described by an equation of motion which reduces to the ordinary sine--Gordon equation when the noncommutation parameter is removed, plus a constraint equation which is nontrivial only in the noncommutative case. We show that the system has an infinite number of conserved currents and we give the general recursive relation for constructing them. For the particular cases of lower spin nontrivial currents we work out the explicit expressions and perform a direct check of their conservation. These currents reduce to the usual sine-Gordon currents in the commutative limit. We find classical ``localized'' solutions to first order in the noncommutativity parameter and describe the Backlund transformations for our system. Finally, we comment on the relation of our noncommutative system to the commutative sine-Gordon system.

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arXiv2001

Superspace approach to anomalous dimensions in {\cal N}=4 SYM

In a {\cal N}=1 superspace setup and using dimensional regularization, we give a general and simple prescription to compute anomalous dimensions of composite operators in {\cal N}=4, SU(N) supersymmetric Yang-Mills theory, perturbatively in the coupling constant g. We show in general that anomalous dimensions are responsible for the appearance of higher order poles in the perturbative expansion of the two-point function and that their lowest contribution can be read directly from the coefficient of the 1/ε^2 pole. As a check of our procedure we rederive the anomalous dimension of the Konishi superfield at order g^2. We then apply this procedure to the case of the double trace, dimension 4, superfield in the 20 of SU(4) recently considered in the literature. We find that its anomalous dimension vanishes for all N in agreement with previous results.

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arXiv2000

Noncommutative Supersymmetric Gauge Anomaly

We extend the general method of hep-th/0009192 to compute the consistent gauge anomaly for noncommutative 4d SSYM coupled to chiral matter. The choice of the minimal homotopy path allows us to obtain a simple and compact result. We perform the reduction to components in the WZ gauge proving that our result contains, as lowest component, the bosonic chiral anomaly for noncommutative YM theories recently obtained in literature.

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arXiv1998

Geometry and beta-functions for N=2 matter models in two dimensions

We study renormalizable nonlinear sigma-models in two dimensions with N=2 supersymmetry described in superspace in terms of chiral and complex linear superfields. The geometrical structure of the underlying manifold is investigated and the one-loop divergent contribution to the effective action is computed. The condition of vanishing beta-function allows to identify a class of models which satisfy this requirement and possess N=4 supersymmetry.

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arXiv1997

The nonminimal scalar multiplet coupled to supersymmetric Yang-Mills

We consider the coupling of nonminimal scalar multiplets to supersymmetric Yang-Mills in four dimensions and compute the one-loop contribution to the low-energy effective action in the abelian sector. We show that the resulting theory realizes the dual version of the corresponding one from N=2 supersymmetric Yang-Mills.

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arXiv1997

The nonminimal scalar multiplet: duality, sigma-model, beta-function

We compute in superspace the one-loop beta-function for the nonlinear sigma-model defined in terms of the nonminimal scalar multiplet. The recently proposed quantization of this complex linear superfield, viewed as the field strength of an unconstrained gauge spinor superfield, allows to handle efficiently the infinite tower of ghosts via the Batalin-Vilkovisky formalism. We find that the classical duality of the nonminimal scalar and chiral multiplets is maintained at the quantum one-loop level.

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arXiv1995

Quantum boundary currents for nonsimply-laced Toda theories

We study the quantum integrability of nonsimply--laced affine Toda theories defined on the half--plane and explicitly construct the first nontrivial higher--spin charges in specific examples. We find that, in contradistinction to the classical case, addition of total derivative terms to the "bulk" current plays a relevant role for the quantum boundary conservation.

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arXiv1992

Quantum symmetries in supersymmetric Toda theories

: We consider two--dimensional supersymmetric Toda theories based on the Lie superalgebras $A(n,n)$, $D(n+1,n)$ and $B(n,n)$ which admit a fermionic set of simple roots and a fermionic untwisted affine extension. In particular, we concentrate on two simple examples, the $B(1,1)$ and $A(1,1)$ theories. Both in the conformal and massive case we address the issue of quantum integrability by constructing the first non trivial conserved currents and proving their conservation to all--loop orders. While the $D(n+1,n)$ and $B(n,n)$ systems are genuine $N=1$ supersymmetric theories, the $A(n,n)$ models possess a global $N=2$ supersymmetry. In the conformal case, we show that the $A(n,n)$ stress--energy tensor, uniquely determined by the holomorphicity condition, has vanishing central charge and it corresponds to the stress--energy tensor of the associated topological theory. (Invited talk at the International Workshop ``String theory, quantum gravity and the unification of the fundamental interactions'', Roma, September 1992)

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arXiv1992

Quantum Conserved Currents in Supersymmetric Toda Theories

We consider $N=1$ supersymmetric Toda theories which admit a fermionic untwisted affine extension, i.e. the systems based on the $A(n,n)$, $D(n+1,n)$ and $B(n,n)$ superalgebras. We construct the superspace Miura trasformations which allow to determine the W-supercurrents of the conformal theories and we compute their renormalized expressions. The analysis of the renormalization and conservation of higher-spin currents is then performed for the corresponding supersymmetric massive theories. We establish the quantum integrability of these models and show that although their Lagrangian is not hermitian, the masses of the fundamental particles are real, a property which is maintained by one-loop corrections. The spectrum is actually much richer, since the theories admit solitons. The existence of quantum conserved higher-spin charges implies that elastic, factorized S-matrices can be constructed.

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