Toy models for wrapping effects

Abstract

The anomalous dimensions of local single trace gauge invariant operators in N=4 supersymmetric Yang-Mills theory can be computed by diagonalizing a long range integrable Hamiltonian by means of perturbative asymptotic Bethe ansatz. This formalism breaks down when the number of fields of the composite operator is smaller than the range of the Hamiltonian which coincides with the order in perturbation theory at study. We analyze two spin chain toy models which might shed some light on the physics behind these wrapping effects. One of them, the Hubbard model, is known to be closely related to N=4 SYM. In this example, we find that the knowledge of the effective spin chain description is insufficient to reconstruct the finite size effects of the underlying electron theory. We compute the wrapping corrections for generic states and relate them to a Luscher like approach. The second toy models are long range integrable Hamiltonians built from the standard algebraic Bethe anstatz formalism. This construction is valid for any symmetry group. In particular, for non-compact groups it exhibits an interesting relation between wrapping interactions and transcendentality.

39 pages, 5 figures

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Cited by in corpus (12)

• Four-loop perturbative Konishi from strings and finite size effects for multiparticle states
• The all loop AdS4/CFT3 Bethe ansatz
• Anomalous dimension with wrapping at four loops in N=4 SYM
• Five-loop Konishi from the Mirror TBA
• Exploring the mirror TBA
• Finite-size effects in the superconformal beta-deformed N=4 SYM
• Finite-Size Effects for Multi-Magnon States
• On Yangian and Long Representations of the Centrally Extended su(2|2) Superalgebra
• Finite-Size Corrections of the ${\mathbb{CP}}^3$ Giant Magnons: the Lüscher terms
• Wrapping corrections for long range spin chains
• Superspace methods for the computation of wrapping effects in the standard and beta-deformed N=4 SYM
• Wrapping effects in supersymmetric gauge theories