New results in the deformed SYM theory

Rossi, G.C.; Sokatchev, E.; Stanev, Yassen S.

doi:10.1016/j.nuclphysb.2005.09.017

Cited by 32 publications

(65 citation statements)

References 20 publications

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“…Motivated by this observation we are led to conjecture that in the large N limit the condition |h| 2 = g 2 is indeed the correct condition for superconformal invariance at any order in perturbation theory. Direct confirmations of this conjecture can be found in the literature up to order g 6 [3,4,5]. Now we give an argument to prove that this is true to all orders.…”

Section: The Exact Anomalous Dimensionssupporting

confidence: 73%

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

Mauri¹,

Penati²,

Santambrogio³

et al. 2005

J. High Energy Phys.

114

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In the β-deformed N = 4 supersymmetric SU (N ) Yang-Mills theory we study the class of operators O J = Tr(Φ J i Φ k ), i = k and compute their exact anomalous dimensions for N, J → ∞. 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 oneloop condition g 2 = hh for superconformal invariance is indeed sufficient to insure the 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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Section: The Exact Anomalous Dimensionssupporting

confidence: 73%

“…In [5] the three loop correction to (2.2) has been also evaluated. Since it turns out to be suppressed for N → ∞, the condition gUsing the equations of motion from the action (2.1) with j =j = 0 (from now on we neglect factors of e ±gV since they are not relevant to our purposes)…”

Section: Introduction 2 Generalitiesmentioning

confidence: 99%

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

Mauri¹,

Penati²,

Santambrogio³

et al. 2005

J. High Energy Phys.

114

View full text Add to dashboard Cite

show abstract

“…More precisely, the generators of the algebra will commute with the Hamiltonian and as such the Hopf algebra will directly be a symmetry of the spin chain 3. There has recently been some controversy regarding the higher-loop finiteness of the marginal deformations beyond the case of real β[21,22,23,24,25]. Although in this work we do take the traditional point of view, based on the validity of the…”

mentioning

confidence: 99%

Quantum symmetries and marginal deformations

Månsson

Zoubos²

2010

J. High Energ. Phys.

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We study the symmetries of the N = 1 exactly marginal deformations of N = 4 Super YangMills theory. For generic values of the parameters, these deformations are known to break the SU(3) part of the R-symmetry group down to a discrete subgroup. However, a closer look from the perspective of quantum groups reveals that the Lagrangian is in fact invariant under a certain Hopf algebra which is a non-standard quantum deformation of the algebra of functions on SU(3). Our discussion is motivated by the desire to better understand why these theories have significant differences from N = 4 SYM regarding the planar integrability (or rather lack thereof) of the spin chains encoding their spectrum. However, our construction works at the level of the classical Lagrangian, without relying on the language of spin chains. Our approach might eventually provide a better understanding of the finiteness properties of these theories as well as help in the construction of their AdS/CFT duals.

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“…Note that computing the difference is much simpler than each term separately, since most of the vector field contributions cancel out. In particular, as far as the chiral propagator is concerned, up to order g 6 , effectively only the superpotential contributes to the difference (for the details see [6]), leaving the quantities…”

Section: The Chiral Propagator To All Ordersmentioning

confidence: 99%

“…The other three vertices receive corrections from non-planar diagrams. Whether they sum up to zero or not is an open question 6 . Only the triple chiral vertex receives also finite planar corrections coming from the second (super)diagram in Figure 3, which as explained in the next subsection modify the chiral propagator at order g 8 .…”

Section: The Three-point Verticesmentioning

confidence: 99%

On the all-order perturbative finiteness of the deformed N=4 SYM theory

2006

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We prove that the chiral propagator of the deformed N = 4 SYM theory can be made finite to all orders in perturbation theory for any complex value of the deformation parameter. For any such value the set of finite deformed theories can be parametrized by a whole complex function of the coupling constant g. We reveal a new protection mechanism for chiral operators of dimension three. These are obtained by differentiating the Lagrangian with respect to the independent coupling constants. A particular combination of them is a CPO involving only chiral matter. Its all-order form is derived directly from the finiteness condition. The procedure is confirmed perturbatively through order g 6 .

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New results in the deformed SYM theory

Cited by 32 publications

References 20 publications

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

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

Quantum symmetries and marginal deformations

On the all-order perturbative finiteness of the deformed N=4 SYM theory

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