Abstract
We study a one parameter family of supersymmetric marginal deformations of \( \mathcal{N}=4 \) SYM with U(1)3 symmetry, known as β-deformations, to understand their dual AdS × X geometry, where X is a large classical geometry in the g 2YM N → ∞ limit. We argue that we can determine whether or not X is geometric by studying the spectrum of open strings between giant gravitons states, as represented by operators in the field theory, as we take N → ∞ in certain double scaling limits. We study the conditions under which these open strings can give rise to a large number of states with energy far below the string scale. The number-theoretic properties of β are very important. When exp(iβ) is a root of unity, the space X is an orbifold. When exp(iβ) close to a root of unity in a double scaling limit sense, X corresponds to a finite deformation of the orbifold. Finally, if β is irrational, sporadic light states can be present.
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Berenstein, D., Dzienkowski, E. Giant gravitons and the emergence of geometric limits in β-deformations of \( \mathcal{N}=4 \) SYM. J. High Energ. Phys. 2015, 126 (2015). https://doi.org/10.1007/JHEP01(2015)126
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DOI: https://doi.org/10.1007/JHEP01(2015)126