Strong coupling anomalous dimensions of Script N = 4 super Yang-Mills

Abstract

We study the strong coupling behaviour of fixed length single trace operators in the scalar SU(2) sector of N = 4 SYM. We assume the recently proposed connection with a twisted half-filled Hubbard model. By explicit direct diagonalization of operators with length L = 4, 6, 8 we study the full perturbative multiplet of those lattice states which have a clear correspondence with gauge theory composite operators. For this multiplet, we follow the weak-strong coupling flow to free fermion states and identify in particular the precise asymptotic fermion configuration. Next, we analyze the Lieb-Wu equations of the twisted Hubbard model. For the antiferromagnetic state we derive its strong coupling expansion working at L up to 32. We also study the lightest state in the perturbative multiplet. This state is non trivial since involves complex solutions of the Lieb-Wu equations. It is particularly interesting for AdS 5 × S 5 duality since it is dual to the folded string semiclassical solution in the thermodynamical limit. We are able to perform the full analysis and compute the next-to-next-to leading terms in the strong coupling expansion for the non trivial lengths L = 12 and L = 20. A general formula is proposed for the NLO expansion for any L = 4(2k + 1), k ∈ N.

Bethe Ansatz solutions for highest states in Script N = 4 SYM and AdS/CFT duality

“…The same leading term is obtained in the Hubbard model formulation of the GBA equations [13,14] (see also [37]). As discussed in [36] this expansion is formal due to the uncontrolled effect of wrapping terms.…”

“…However, the Hubbard model formulation [12] suggests that this scenario is not entirely satisfactory. There, limit ambiguities and wrapping problems are absent and nevertheless the same prediction ∆/L ∼ √ λ/π 2 is recovered including the prefactor [13,14]. A more convincing proof should at least include the analysis of the solution of the SBA equations, valid in the strong coupling limit.…”

“…The scaling operator is well known, at least in the L → ∞ limit and is the double contour solution of the GBA equations described in [38]. It has been studied in some details also in the Hubbard model formulation [14]. Setting, as usual λ = λ/J 2 we have…”

АдС/Ктп-Дуальность В Режиме Сильной Связи

“…Это значительно редуцирует гиль-бертово пространство. Например, было показано, что в наполовину заполненной решетке при L = 8 полная размерность уменьшается с 4900 до 226 [17]. Зависящий от взаимодействия спектральный поток вычислялся численно с помощью метода…”

“…Роль этих лишних состояний остается неясной, а потому ниже мы рассматриваем зависимость от константы связи только для та-ких состояний, которые при λ = 0 приводят к состояниям без двойного заполнения, т.е. состояниям, имеющим классические аномальные размерности ∆(λ = 0) = L (пертурбативный мультиплет в работе [17]). Тем не менее с ростом 'т хофтовской константы связи эти состояния начинают смешиваться со всеми дополнительными состояниями с двойным заполнением.…”