Quantum Symmetries and Marginal Deformations

Abstract

We study the symmetries of the N=1 exactly marginal deformations of N=4 Super Yang-Mills theory. For generic values of the parameters, these deformations are known to break the SU(3) part of the R-symmetry group down to a discrete subgroup. However, a closer look from the perspective of quantum groups reveals that the Lagrangian is in fact invariant under a certain Hopf algebra which is a non-standard quantum deformation of the algebra of functions on SU(3). Our discussion is motivated by the desire to better understand why these theories have significant differences from N=4 SYM regarding the planar integrability (or rather lack thereof) of the spin chains encoding their spectrum. However, our construction works at the level of the classical Lagrangian, without relying on the language of spin chains. Our approach might eventually provide a better understanding of the finiteness properties of these theories as well as help in the construction of their AdS/CFT duals.

1+40 pages. v2: minor clarifications and references added. v3: Added an appendix, fixed minor typos

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Cited by in corpus (14)

• Review of AdS/CFT Integrability, Chapter IV.2: Deformations, Orbifolds and Open Boundaries
• On Marginal Deformations and Non-Integrability
• Yangians, S-matrices and AdS/CFT
• Marginal deformations of 3d $\mathcal{N}=2$ CFTs from AdS${}_4$ backgrounds in generalised geometry
• Dynamical Spin Chains in 4D $\mathcal{N}=2$ SCFTs
• Fast spinning strings on $\eta$ deformed $Ad{S}_5\times S^5$
• Boost generator in AdS_3 integrable superstrings for general braiding
• Y-system for $\gamma$-deformed ABJM Theory
• The dual string sigma-model of the SU_q(3) sector
• Untwisting the symmetries of $\beta$-deformed Super-Yang--Mills
• Integrability of Orbifold ABJM Theories
• Marginal deformations and quasi-Hopf algebras
• Supergraphs and the cubic Leigh-Strassler model
• Bilocal phase operators in beta-deformed super Yang-Mills