We study the null polygonal Wilson loops/gluon scattering amplitudes in planar <math><mi>N</mi><mo>=</mo><mn>4</mn></math> SYM by means of the pentagon Operator Product Expansion (OPE) series and its integrability features, with particular attention on the strong coupling expansion. Actually, at all couplings and for the hexagon we disentangle the <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>4</mn><mo>)</mo></math> matrix structure of the squared form factors for fermions, organising them in Young diagrams similar to those previously used for scalars. Then, we concentrate on the strong coupling regime and show the appearance of a new (effective) particle in the series: the fermion-antifermion bound state, the so-called ‘meson’. Of course, we identify its interaction with itself in the OPE series, with formation of (effective) bound states, and with the gluons and bound states of them. All together these extract from the OPE series the <math><mi>A</mi><mi>d</mi><msub><mrow><mi>S</mi></mrow><mrow><mn>5</mn></mrow></msub></math> minimal area result for the Wilson loop, described by a set of Thermodynamic Bethe Ansatz (TBA)-like equations, and highlight also all the one-loop contributions. Moreover, the same strategy applies to <math><mi>N</mi><mo>=</mo><mn>2</mn></math> Nekrasov partition function via the parallel meson/instanton. Eventually, to complete the strong coupling analysis, we consider the scalar sector for any polygon, confirming the emergence of a non-perturbative contribution from the string in <math><msup><mrow><mi>S</mi></mrow><mrow><mn>5</mn></mrow></msup></math>, which eludes and corrects the minimal area argument.

Italy

Alfredo Bonini

Davide Fioravanti

Japan

Simone Piscaglia

Marco Rossi

Fermions and scalars in Wilson loops at strong coupling and beyond

We disentangle the contribution of scalars to the OPE series of null hexagonal Wilson loops/MHV gluon scattering amplitudes in multicolour <math><mi>N</mi><mo>=</mo><mn>4</mn></math> SYM. In specific, we develop a systematic computation of the <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>4</mn><mo>)</mo></math> matrix part of the Wilson loop by means of Young tableaux (with several examples). 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 <math><mi>A</mi><mi>d</mi><msub><mrow><mi>S</mi></mrow><mrow><mn>5</mn></mrow></msub></math> string contribution).

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

Previously predicted by the S -matrix bootstrap of the excitations over the GKP quantum vacuum, the appearance of a new particle at strong coupling — formed by one fermion and one anti-fermion — is here confirmed: this two-dimensional meson shows up, along with its infinite tower of bound states, while analysing the fermionic contributions to the Operator Product Expansion (collinear regime) of the Wilson null polygon loop. Moreover, its existence, free (This term is used here as opposite to bound, thus as unbound) and bound, turns out to be a powerful idea in re-summing all the contributions (at large coupling) for a general n -gon ( n ≥ 6) to a Thermodynamic Bethe Ansatz, which is proven to be equivalent to the known one and suggests new structures for a special Y -system.