The generalised scaling function: A note

Fioravanti, Davide; Grinza, Paolo; Rossi, Marco

doi:10.1016/j.nuclphysb.2009.10.007

Cited by 21 publications

(24 citation statements)

References 32 publications

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“…Closely related examples are the generalized scaling function, proposed in [49], and the generalized cusp anomalous dimension (or equivalently the quark-antiquark potential), studied in [50][51][52][53][54]. As studied in [33,[55][56][57], the strong coupling analysis of the generalized scaling function is almost in parallel with the cusp anomalous dimension, and thus it is a good exercise to see its resurgent aspect along the line in this paper. The analysis of the generalized cusp anomalous dimension will be much more involved.…”

Section: Discussionmentioning

confidence: 84%

Resurgence of the cusp anomalous dimension

Dorigoni¹,

Hatsuda²

2015

J. High Energ. Phys.

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We revisit the strong coupling limit of the cusp anomalous dimension in planar N = 4 super Yang-Mills theory. It is known that the strong coupling expansion is asymptotic and non-Borel summable. As a consequence, the cusp anomalous dimension receives non-perturbative corrections, and the complete strong coupling expansion should be a resurgent transseries. We reveal that the perturbative and non-perturbative parts in the transseries are closely interrelated. Solving the Beisert-Eden-Staudacher equation systematically, we analyze in detail the large order behavior in the strong coupling perturbative expansion and show that the non-perturbative information is indeed encoded there. An ambiguity of (lateral) Borel resummations of the perturbative expansion is precisely canceled by the contributions from the non-perturbative sectors, and the final result is real and unambiguous.

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Section: Discussionmentioning

confidence: 84%

Resurgence of the cusp anomalous dimension

Dorigoni¹,

Hatsuda²

2015

J. High Energ. Phys.

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“…r (g) is the (coefficient of the) first generalised scaling density [22,23,24,25,26] and the extra coefficients S extra r (g) are solutions of the following system…”

Section: All Loops Resultsmentioning

confidence: 99%

Beyond cusp anomalous dimension from integrability

2009

Self Cite

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We study the first sub-leading correction O((ln s) 0 ) to the cusp anomalous dimension in the high spin expansion of finite twist operators in N = 4 SYM theory. Since this approximation is still governed by a linear integral equation (derived already from the Bethe Ansatz equations in a previous paper), we finalise it better in order to study the weak and strong coupling regimes. In fact, we emphasise how easily the weak coupling expansion can be obtained, confirms the known four loop result and predicts the higher orders. Eventually, we pay particular attention to the strong coupling regime showing agreement and predictions in comparison with string expansion; speculations on the 'universal' part (upon subtracting the collinear anomalous dimension) are brought forward.

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“…where dots stand for subleading corrections, and it is not difficult to give, see for instance [21], the values of the first two coefficients of the expansion of c 0 :…”

Section: Jhep11(2009)037mentioning

confidence: 99%

“…As in the one loop case, it is easy to give (see [21]) the first orders in the expansion of c in the limit (1.4):…”

Section: Jhep11(2009)037mentioning

confidence: 99%

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Study on Focusing Mechanism of Radial Polarization with Immersion Objective

Lan¹,

Tien

2008

jjap

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We describe a procedure for determining the generalised scaling functions f n (g) at all the values of the coupling constant. These functions describe the high spin contribution to the anomalous dimension of large twist operators (in the sl(2) sector) of N = 4 SYM. At fixed n, f n (g) can be obtained by solving a linear integral equation (or, equivalently, a linear system with an infinite number of equations), whose inhomogeneous term only depends on the solutions at smaller n. In other words, the solution can be written in a recursive form and then explicitly worked out in the strong coupling regime. In this regime, we also emphasise the peculiar convergence of different quantities ('masses', related to the f n (g)) to the unique mass gap of the O(6) nonlinear sigma model and analyse the first next-to-leading order corrections.ArXiv ePrint: 0808.1886 Furthermore, the same linear integral equation (2.11) still controls this next-to-leading order (nlo), f (0) (g, j). Now, similarly, we may imagine that the dots should initially be inverse integer powers of ln s, with coefficients, at each power, depending on g and j. Afterwards, inverse integer powers of s should also enter the stage, but they are determined by the complete non-linear integral equation (NLIE) of [18]. 1 However, in this paper we will constrain ourselves to the leading Sudakov factor f (g, j), leaving the analysis of its corrections for future publications.Actually, in [19] we have initiated the study of the strong coupling regime of the first generalised scaling function f 1 (g) and have shown the proportionality of its leading order to the mass gap m(g) (see (3.13) below) of the O(6) nonlinear sigma model (NLSM). This gives a first positive test, in the strong coupling regime j ≪ m(g) of the NLSM, for the Alday-Maldacena proposal [11]. This claims that as long as g ≫ j the quantity f (g, j) + j should coincide with the O(6) NLSM energy density. The latter was expanded and checked for the first orders in the perturbative regime j ≫ m(g) of the NLSM by [11]. Hence, our test was a first indication in another valuable region of the NLSM, i.e. j ≪ m(g), where the free energy series is, besides, convergent [22]. Afterwards, the embedding of the O(6) NLSM into N = 4 SYM at large g was brilliantly shown in a formal way by [20], where the leading strong coupling contribution of f 3 (g) was computed too. In a contemporaneous paper [21], starting from the our linear integral equation [19], we have set down the initial ideas for a systematic study of all the f n (g) and confined our study to the first four f 1 (g), f 2 (g), f 3 (g) and f 4 (g), by finding for them some analytic relations and expressions. These have been then evaluated numerically with additional analytic results for large g, finding agreement with the suitable results from the O(6) NLSM [22]. Furthermore, the agreement on f 4 (g) is highly nontrivial, since it contains the details of the specific interaction in the O(6) NLSM. For completeness sake, all these results will be reported in the f...

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The generalised scaling function: A note

Cited by 21 publications

References 32 publications

Resurgence of the cusp anomalous dimension

Resurgence of the cusp anomalous dimension

Beyond cusp anomalous dimension from integrability

Study on Focusing Mechanism of Radial Polarization with Immersion Objective

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