TBA-like equations and Casimir effect in (non-)perturbative AdS/CFT

Fioravanti, Davide; Rossi, Marco

doi:10.1007/jhep12(2012)013

Cited by 12 publications

(23 citation statements)

References 94 publications

(233 reference statements)

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“…In detail, these excitations are gluons with their bound states, fermions and antifermions and scalars which scatter in a non-trivial way [36,37]. Consequently, in order to pursue the OPE project, we need to know the dispersion laws of the GKP string excitations [36] and the 2D scattering factors between them [37,38,39]. And, although with more ambitious plans in mind, we shall first scrutinise regimes where explicit computations are possible.…”

Section: Connected Functions 49 1 Introduction and Summarymentioning

confidence: 99%

The contribution of scalars to N=4 SYM amplitudes II: Young tableaux, asymptotic factorisation and strong coupling

Bonini¹,

Fioravanti²,

Piscaglia³

et al. 2018

Nuclear Physics B

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We disentangle the contribution of scalars to the OPE series of null polygonal Wilson loops/MHV gluon scattering amplitudes in multicolour N = 4 SYM. In specific, we develop a systematic computation of the SO(6) matrix part of the Wilson loop by means of Young tableaux (with several examples too). Then, we use a peculiar factorisation property (when a group of rapidities becomes large) to deduce an explicit polar form. Furthermore, we emphasise the advantages of expanding the logarithm of the Wilson loop in terms of 'connected functions' as we apply this procedure to find an explicit strong coupling expansion (definitively proving that the leading order can prevail on the classical AdS 5 string contribution). Dedicated to the memory of Yassen Stanev

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Section: Connected Functions 49 1 Introduction and Summarymentioning

confidence: 99%

The contribution of scalars to N=4 SYM amplitudes II: Young tableaux, asymptotic factorisation and strong coupling

Bonini¹,

Fioravanti²,

Piscaglia³

et al. 2018

Nuclear Physics B

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“…In specific, the excitations appearing in the series are multiparticle states: gluons and bound states, fermions, antifermions and, finally, scalars. Therefore, in order to pursue this strategy, one needs to know the dispersion laws of the GKP string excitations [34] and the 2d scattering factors [35,36,37] between them 1 .The validity of the OPE series has been checked, by explicit computations, in two different regimes. These are the weak (e.g.…”

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confidence: 99%

Fermions and scalars in N=4 Wilson loops at strong coupling and beyond

et al. 2019

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We study the strong coupling behaviour of null polygonal Wilson loops/gluon amplitudes in N = 4 SYM, by using the OPE series and its integrability features. For the hexagon we disentangle the SU (4) matrix structure of the form factors for fermions, organising them in a pattern similar to the Young diagrams used previously for the scalar sector [1,2]. Then, we complete and extend the discussion of [3] by showing, at strong coupling, the appearance of a new effective particle in the series: the fermion-antifermion bound state, the so-called meson. We discuss its interactions in the OPE series with itself by forming (effective) bound states and with the gluons and bound states of them. These lead the OPE series to the known AdS 5 minimal area result for the Wls, described in terms of a set of TBA-like equations. This approach allows us to detect all the one-loop contributions and, once the meson has formed, applies to N = 2 Nekrasov partition function via the parallel meson/instanton (in particular, they share the mechanism by which their bound states emerge and form the TBA node). Finally, to complete the strong coupling analysis, we consider the scalar sector for any polygon, confirming the emergence of a leading contribution from the non-perturbative theory on the sphere S 5In the realm of the supersymmetric gauge theories a special role is played by N = 4 Super Yang-Mills (SYM), with gauge group SU (N c ) and dimensionless coupling constant g Y M . The theory indeed appears at one side of the most known example of AdS/CFT correspondence [4,5,6], i.e. the duality between type IIB superstring theory on AdS 5 × S 5 and N = 4 SYM on the boundary of AdS 5 , the 4d Minkowski spacetime.Of particular interest is the planar limit N c → ∞, in which we also send g Y M → 0 keeping the 't Hooft coupling λ ≡ N c g 2 Y M fixed. The new coupling λ is the only parameter of the planar theory and in literature it is often represented as λ = 16π 2 g 2 . The planar N = 4 SYM shows remarkable connections with 1+1 dimensional integrable models [7,8,9,10,11,12,13,14,15,16,17,18], which have allowed a better comprehension and partial proof of the aforementioned correspondence.Historically, integrability was discovered when dealing with the spectral problem, i.e. the computation of the anomalous dimension of local gauge invariant operators. More recently, it played an important role also in the evaluation of null polygonal Wilson loops (Wls). They have been proposed to be dual to gluon scattering amplitudes [19,20,21], which makes them even more interesting. Currently, this correspondence has been widely tested both at weak and strong coupling, so that it can be considered a well-established fact.In any conformal quantum field theory, the Operator Product Expansion (OPE) technique can be applied, besides to the usual product of local operators, also to the null polygonal Wilson loops [22]. This method has an intrinsic non-perturbative nature and recalls the Form Factor (FF) Infra-Red (IR) spectral series of the correlation functions in ...

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“…On the same footing, we start wondering in [21] about the scattering S-matrix which may be attached to the two-particle states (of, at least, twist-4)…”

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Asymptotic Bethe Ansatz on the GKP vacuum as a defect spin chain: Scattering, particles and minimal area Wilson loops

2015

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Moving from Beisert-Staudacher equations, the complete set of Asymptotic Bethe Ansatz equations and S-matrix for the excitations over the GKP vacuum is found. The resulting model on this new vacuum is an integrable spin chain of length R = 2 ln s (s = spin) with particle rapidities as inhomogeneities, two (purely transmitting) defects and SU (4) (residual R-)symmetry. The non-trivial dynamics of N = 4 SYM appears in elaborated dressing factors of the 2D two-particle scattering factors, all depending on the 'fundamental' one between two scalar excitations. From scattering factors we determine bound states. In particular, we study the strong coupling limit, in the non-perturbative, perturbative and giant hole regimes. Eventually, from these scattering data we construct the 4D pentagon transition amplitudes (perturbative regime). In this manner, we detail the multi-particle contributions (flux tube) to the MHV gluon scattering amplitudes/Wilson loops (OPE or BSV series) and re-sum them to the Thermodynamic Bubble Ansatz. *

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TBA-like equations and Casimir effect in (non-)perturbative AdS/CFT

Cited by 12 publications

References 94 publications

The contribution of scalars to N=4 SYM amplitudes II: Young tableaux, asymptotic factorisation and strong coupling

The contribution of scalars to N=4 SYM amplitudes II: Young tableaux, asymptotic factorisation and strong coupling

Fermions and scalars in N=4 Wilson loops at strong coupling and beyond

Asymptotic Bethe Ansatz on the GKP vacuum as a defect spin chain: Scattering, particles and minimal area Wilson loops

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