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Two-loop world-sheet corrections in AdS_5 x S^5 superstring

R. Roiban, A. Tirziu, A. A. Tseytlin

TL;DR

This work initiates a two-loop analysis of quantum corrections to the AdS5×S5 superstring in a homogeneous background linked to the long-string limit, aiming to test the strong-coupling structure of the AdS/CFT Bethe ansatz. Using conformal gauge and two κ-symmetry gauges, the authors compute bosonic and fermionic contributions to the 2-loop world-sheet effective action, confronting UV divergences and gauge-regularization issues. The key result is that the finite part of the total 2-loop correction is proportional to Catalan's constant K, and with the fermionic contribution interpreted appropriately (cF = −2), the subleading coefficient a2 in the cusp anomalous dimension scaling function matches the BES equation value a2 = −K/π. This provides a nontrivial cross-check of the exact Bethe Ansatz structure at strong coupling, despite unresolved questions about complete UV finiteness and gauge dependence in the intermediate steps.

Abstract

We initiate the computation of the 2-loop quantum AdS_5 x S^5 string corrections on the example of a certain string configuration in S^5 related by an analytic continuation to a folded rotating string in AdS_5 in the ``long string'' limit. The 2-loop term in the energy of the latter should represent the subleading strong-coupling correction to the cusp anomalous dimension and thus provide a further check of recent conjectures about the exact structure of the Bethe ansatz underlying the AdS/CFT duality. We use the conformal gauge and several choices of the κ-symmetry gauge. While we are unable to verify the cancellation of 2d UV divergences we compute the bosonic contribution to the effective action and also determine the non-trivial finite part of the fermionic contribution. Both the bosonic and the fermionic contributions to the string energy happen to be proportional to the Catalan's constant. The resulting value for 2-loop superstring prediction for the subleading coefficient a_2 in the scaling function matches the numerical value found in hep-th/0611135 from the BES equation.

Two-loop world-sheet corrections in AdS_5 x S^5 superstring

TL;DR

This work initiates a two-loop analysis of quantum corrections to the AdS5×S5 superstring in a homogeneous background linked to the long-string limit, aiming to test the strong-coupling structure of the AdS/CFT Bethe ansatz. Using conformal gauge and two κ-symmetry gauges, the authors compute bosonic and fermionic contributions to the 2-loop world-sheet effective action, confronting UV divergences and gauge-regularization issues. The key result is that the finite part of the total 2-loop correction is proportional to Catalan's constant K, and with the fermionic contribution interpreted appropriately (cF = −2), the subleading coefficient a2 in the cusp anomalous dimension scaling function matches the BES equation value a2 = −K/π. This provides a nontrivial cross-check of the exact Bethe Ansatz structure at strong coupling, despite unresolved questions about complete UV finiteness and gauge dependence in the intermediate steps.

Abstract

We initiate the computation of the 2-loop quantum AdS_5 x S^5 string corrections on the example of a certain string configuration in S^5 related by an analytic continuation to a folded rotating string in AdS_5 in the ``long string'' limit. The 2-loop term in the energy of the latter should represent the subleading strong-coupling correction to the cusp anomalous dimension and thus provide a further check of recent conjectures about the exact structure of the Bethe ansatz underlying the AdS/CFT duality. We use the conformal gauge and several choices of the κ-symmetry gauge. While we are unable to verify the cancellation of 2d UV divergences we compute the bosonic contribution to the effective action and also determine the non-trivial finite part of the fermionic contribution. Both the bosonic and the fermionic contributions to the string energy happen to be proportional to the Catalan's constant. The resulting value for 2-loop superstring prediction for the subleading coefficient a_2 in the scaling function matches the numerical value found in hep-th/0611135 from the BES equation.

Paper Structure

This paper contains 11 sections, 195 equations, 1 figure.

Table of Contents

  1. Introduction
  2. String background and strong-coupling expansion of minimal twist anomalous dimension
  3. One-loop approximation
  4. Structure of the paper
  5. Bosonic contribution to the 2-loop effective action
  6. General remarks on bosonic sigma model
  7. $AdS_5 \times S^5$ sigma model fluctuation action
  8. Structure of 2-loop quantum corrections
  9. Evaluation of 2-loop momentum integrals
  10. Fermionic contribution to the 2-loop effective action
  11. Concluding remarks

Figures (1)

  • Figure 1: Two-loop contributions (momentum conservation $q_i+q_j+q_k=0$ is assumed).