Structure constants of β deformed super Yang-Mills

David, Justin R.; Sadhukhan, Abhishake

doi:10.1007/jhep10(2013)206

Cited by 4 publications

(3 citation statements)

References 72 publications

(136 reference statements)

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“…Concretely, the planar anomalous dimensions of the operators Õk were argued to vanish in [177], generalising an argument of [254,255] for rational β. Moreover, three-point functions Õk Õk ′ Õk ′′ were studied in [256] at one-loop order in the planar gauge theory as well as at strong coupling via the Lunin-Maldacena background and found to be independent of β.…”

Section: Relation To the Undeformed Theorymentioning

confidence: 99%

Form factors and the dilatation operator in $\mathcal{N}=4$ super Yang-Mills theory and its deformations

Wilhelm¹

2016

Preprint

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For more than half a century, quantum field theory (QFT) has been the most accurate and successful framework to describe the fundamental interactions among elementary particles, albeit with the notable exception of gravity. Nevertheless, QFTs are in general far from being completely understood. This is due to a lack of calculational techniques and tools as well as our limited understanding of the mathematical structures that emerge in them. In the last one and a half decades, tremendous progress has been made in understanding certain aspects of a particular QFT, namely the maximally supersymmetric Yang-Mills theory in four dimensions, termed N = 4 SYM theory, which has risen the hope that this theory could be exactly solvable. In particular, this progress occurred for scattering amplitudes due to the development of on-shell methods and for correlation functions of gauge-invariant local composite operators due to integrability. In this thesis, we address the question to which extend the methods and structures found there can be generalised to other quantities in the same theory and to other theories.Form factors describe the overlap between a gauge-invariant local composite operator on the one hand and an asymptotic on-shell scattering state on the other hand. Thus, they form a bridge between the purely off-shell correlation functions and the purely onshell scattering amplitudes. In the first part of this thesis, we calculate form factors of general, protected as well as non-protected, operators at various loop orders and numbers of external points in N = 4 SYM theory. This is achieved using many of the successful onshell methods that were developed in the context of scattering amplitudes, albeit after some important extensions. In particular, we show how form factors and on-shell methods allow us to obtain the dilatation operator, which yields the spectrum of anomalous dimensions of composite operators and acts as Hamiltonian of the integrable spin chain of the spectral problem. At one-loop level, we calculate the cut-constructible part of the form factor with minimal particle multiplicity for any operator using generalised unitarity and obtain the complete one-loop dilatation operator from it. We demonstrate that on-shell methods and form factors can be used to calculate the dilatation operator also at higher loop orders, using the Konishi operator and the SU(2) sector at two loops as examples. Remarkably, the finite remainder functions of the latter form factors possess universal properties with respect to their transcendentality. Moreover, form factors of non-protected operators share many features of scattering amplitudes in QCD, such as UV divergences and rational terms. At tree level, we show how to construct form factors via extended on-shell diagrams, a Graßmannian integral as well as the integrability-based technique of R operators. Using the latter technique, form factors can be constructed as eigenstates of an integrable transfer matrix, which implies the existence of a tower of conserved charges.Defor...

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Section: Relation To the Undeformed Theorymentioning

confidence: 99%

Form factors and the dilatation operator in $\mathcal{N}=4$ super Yang-Mills theory and its deformations

Wilhelm¹

2016

Preprint

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“…In contrast to the Konishi operator, the operators O k themselves are altered by the * -deformation. 10 In [44], the three-point functions O k O k ′ O k ′′ of the deformed operators were investigated at one-loop order in the planar gauge theory and at strong coupling in the Lunin-Maldacena background. In these regimes, they were found to be independent of β.…”

Section: Filk's Theorem In the β-Deformationmentioning

confidence: 99%

The complete one-loop dilatation operator of planar real β-deformed N $$ \mathcal{N} $$ = 4 SYM theory

Fokken

Sieg

Wilhelm

2014

J. High Energ. Phys.

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Abstract:We determine the missing finite-size corrections to the asymptotic one-loop dilatation operator of the real β-deformed N = 4 SYM theory for the gauge groups U(N ) and SU(N ) in the 't Hooft limit. In the SU(N ) case, the absence of the U(1) field components leads to a new kind of finite-size effect, which we call prewrapping. We classify which states are potentially affected by prewrapping at generic loop orders and comment on the necessity to include it into the integrability-based description. As a further result, we identify classes of n-point correlation functions which at all loop orders in the planar theory are given by the values of their undeformed counterparts. Finally, we determine the superconformal multiplet structure and one-loop anomalous dimensions of all single-trace states with classical scaling dimension ∆ 0 ≤ 4.5.

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“…This argument ties the non-renormalization of the 3-point extremal functions to the nonrenormalization of the Kälher potential on moduli space and seems to be different in spirit to the arguments on Harmonic superspace [90] (see also [91,92] and references therein and see also [93] for the study of β-deformations). Notice that this is not expected to be true in three dimensional field theories of ABJM type [94] (the corresponding field theories can be found in [95]).…”

Section: Discussionmentioning

confidence: 96%

Extremal chiral ring states in the AdS/CFT correspondence are described by free fermions for a generalized oscillator algebra

Berenstein

2015

Phys. Rev. D

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This paper studies a special class of states for the dual conformal field theories associated with supersymmetric AdS 5 ×X compactifications, where X is a Sasaki-Einstein manifold with additional U(1) symmetries. Under appropriate circumstances, it is found that elements of the chiral ring that maximize the additional U(1) charge at fixed R-charge are in one to one correspondence with multitraces of a single composite field. This is also equivalent to Schur functions of the composite field. It is argued that in the formal zero coupling limit that these dual field theories have, the different Schur functions are orthogonal. Together with large N counting arguments, one predicts that various extremal three point functions are identical to those of N = 4 SYM, except for a single normalization factor, which can be argued to be related to the R-charge of the composite word. The leading and subleading terms in 1/N are consistent with a system of free fermions for a generalized oscillator algebra. One can further test this conjecture by constructing coherent states for the generalized oscillator algebra that can be interpreted as branes exploring a subset of the moduli space of the field theory and use these to compute the effective Kähler potential on this subset of the moduli space.

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Structure constants of β deformed super Yang-Mills

Cited by 4 publications

References 72 publications

Form factors and the dilatation operator in $\mathcal{N}=4$ super Yang-Mills theory and its deformations

Form factors and the dilatation operator in $\mathcal{N}=4$ super Yang-Mills theory and its deformations

The complete one-loop dilatation operator of planar real β-deformed N $$ \mathcal{N} $$ = 4 SYM theory

Extremal chiral ring states in the AdS/CFT correspondence are described by free fermions for a generalized oscillator algebra

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