Star product and the general Leigh–Strassler deformation

Bundzik, Daniel

doi:10.1088/1126-6708/2007/04/035

Cited by 6 publications

(18 citation statements)

References 17 publications

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“…Using the twist, we also introduced a star product which relates the Leigh-Strassler lagrangian to that of N = 4 SYM, as well as its inverse, which deforms the N = 4 SYM lagrangian to the Leigh-Strassler one. This generalises previously known star products [7,20,21] which were only applicable to integrable cases, such as the β or w-deformation.…”

Section: Discussionsupporting

confidence: 84%

Marginal deformations and quasi-Hopf algebras

Dlamini¹,

Zoubos²

2019

J. Phys. A: Math. Theor.

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We establish the existence of a quasi-Hopf algebraic structure underlying the Leigh-Strassler N = 1 superconformal marginal deformations of the N = 4 Super-Yang-Mills theory. The scalar-sector R-matrix of these theories, which is related to their one-loop spin chain Hamiltonian, does not generically satisfy the Quantum Yang-Baxter Equation. By constructing a Drinfeld twist which relates this R-matrix to that of the N = 4 SYM theory, but also produces a non-trivial co-associator, we show that the generic Leigh-Strassler R-matrix satisfies the quasi-Hopf version of the QYBE. We also use the twist to define a suitable star product which directly relates the N = 4 SYM superpotential to that of the marginally deformed gauge theories. We expect our results to be relevant to studies of integrability (and its breaking) in these theories, as well as to provide useful input for supergravity solution-generating techniques.

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Section: Discussionsupporting

confidence: 84%

Marginal deformations and quasi-Hopf algebras

Dlamini¹,

Zoubos²

2019

J. Phys. A: Math. Theor.

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“…As in the undeformed case, vibrations of the giant in the AdS directions δx a decouple from the rest of the fluctuations, and minimizing the second order action subject to the first order constraint ν = 0 leads to the spectrum 16) which is manifestly positive definite. The coupled radial and null fluctutations, δr and δx − respectively, satisfy the linear system of equations…”

Section: Deformed Giantsmentioning

confidence: 99%

“…For a recent extension of this star product to capture a more general form of the Leigh Strassler deformation see[16] 4 The superconformal Lunin-Maldacena deformation then, is a special case in which all three tori are deformed by the same amount, γ1 = γ2 = γ3 = γ…”

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confidence: 99%

Giant gravitons on deformed pp-waves

Hamilton¹,

Murugan²

2007

J. High Energy Phys.

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Abstract:The recently constructed Lunin-Maldacena deformation of AdS 5 × S 5 is known to support two inequivalent Penrose limits that lead to BPS pp-wave geometries. In this note, we construct new giant graviton solutions on these backgrounds. A detailed study of the spectra of small fluctuations about these solutions reveals a remarkably rich structure. In particular, the giants that we contruct fall into two classes, one of which appears to remain stable in the Penrose limit independently of the strength of the deformation. The other class of giants, while more difficult to treat analytically, seems to exhibit a shape deformation not unlike the so-called "squashed giants" seen in the pp-wave with a constant NS B-field turned on. Some consideration is also given to the associated giant operators in the BMN limit of the dual N = 1 SYM gauge theory.

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“…Marginal deformations of conformally invariant supersymmetric gauge theories were first systematically studied by Leigh and Strassler [17], and have subsequently been analyzed extensively both perturbatively and at strong coupling in [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33] just to mention a few.…”

Section: β-Deformed Super Yang-mills Theorymentioning

confidence: 99%

“…The upshot of the preceding section was that the N = 4 and β-deformed theories have identical planar sectors up to simple phase factors, which for any given amplitude to all orders in perturbation theory are determined by the configuration of its external legs and their U(1) 1 × U(1) 2 symmetry charges according to (33). The logical solution is therefore to take the N = 4 superamplitude and just attach to each component the appropriate phase factor.…”

Section: A Mhv Generating Functionsmentioning

confidence: 99%

Bilocal phase operators inβ-deformed super Yang-Mills

Søgaard¹

2012

Phys. Rev. D

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We present tree-level scattering amplitudes in β-deformed super Yang-Mills theory in terms of new generating functions, derived by construction of a phase operator and application thereof to the N = 4 superamplitudes. The technique is explicitly illustrated for the MHV and NMHV sectors. Along these lines we propose a phase representation of the N = 4 superconformal algebra realized on deformed amplitudes in the planar limit. Validity of the MHV vertex expansion is proven and a connection to non-planar multi-loop unitarity cuts is established. Our derivations are also compatible with the related γ-deformation.

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Star product and the general Leigh–Strassler deformation

Cited by 6 publications

References 17 publications

Marginal deformations and quasi-Hopf algebras

Marginal deformations and quasi-Hopf algebras

Giant gravitons on deformed pp-waves

Bilocal phase operators inβ-deformed super Yang-Mills

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