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Light-Like Cusp Anomaly and the Interpolating Function in ABJM

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Perturbative and Non-perturbative Approaches to String Sigma-Models in AdS/CFT

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Abstract

The first significative difference is the absence of maximal supersymmetry of the \({AdS_4\times \mathbb {CP}^3}\) background, which complicates the construction of the corresponding superstring action.

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Notes

  1. 1.

    See also discussions in [10,11,12].

  2. 2.

    The scaling function is identified with twice the null cusp anomalous dimension, governing the UV divergences of a light-like Wilson cusp. This is explained at length in the particular case of \(\mathcal {N}=4\) SYM in Sect. 7.1 in the next chapter.

  3. 3.

    The relation between the gauge-theory ’t Hooft coupling \(\lambda _{\text {ABJM}}\) and the string tension T is sensitive to the regularization choice in the two theories. The consistency of our result suggests that regularization behind the conjectured form of \(h(\lambda )\) and the worldsheet regularization in the two-loop calculation effectively capture the same physics, see also [3, 19] for related discussions. We thank Radu Roiban for this remark.

  4. 4.

    Alternatively, one could still use the coset action of [48, 49]—which is not suitable when strings move confined in AdS [49, 50]—starting with a classical solution spinning both in \(AdS_4\) with spin S and in \(\mathbb {CP}^3\) with spin J, and taking on the resulting expression for the one-loop energy a smooth \(J\rightarrow 0\) limit [36].

  5. 5.

    To see this, compare the expressions for (\(x^+,x^-,w\)) in (6.14) with the ones for (\(x^+,x^-,z\)) in (7.12), where the latter is shown in Fig. 7.2.

  6. 6.

    We introduce the factor 2 in the field \(x^1\) to normalize the kinetic term of \(\tilde{x}^1\), cf. (7.14).

  7. 7.

    This is related to coordinate transformations and field redefinitions occurring between the GKP string [58], whose energy is given in terms of \(f_\mathrm{YM}(\lambda _\mathrm{YM})\), and the null cusp solution in the Poincaré patch used here, see discussion in [55].

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  1. Institute of Physics, University of São Paulo, São Paulo, São Paulo, Brazil

    Edoardo Vescovi

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Vescovi, E. (2017). Light-Like Cusp Anomaly and the Interpolating Function in ABJM. In: Perturbative and Non-perturbative Approaches to String Sigma-Models in AdS/CFT. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-63420-3_6

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