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On one-loop correction to energy of spinning strings in S^5

S. A. Frolov, I. Y. Park, A. A. Tseytlin

TL;DR

This work investigates the one-loop correction to the energy of a circular spinning string in S^5 within AdS/CFT, focusing on the leading 1/J term governed by the coefficient d1 in the semiclassical energy expansion. The authors refine the theoretical treatment of E1, address singularities in fluctuation frequencies, and implement a convergent regularization to extract d1 numerically across a range of q and winding k. Their results reveal nontrivial q–k dependence, including zeros of d1 in the stable region, and indicate a discrepancy with gauge-theory predictions, particularly in the unstable q=1 case. They argue that order-of-limits or wrapping effects may underlie the mismatch, with implications for Bethe Ansatz approaches to the quantum string spectrum and for reconciling string and gauge descriptions in the 1/J regime.

Abstract

We revisit the computation (hep-th/0306130) of 1-loop AdS_5 x S^5 superstring sigma model correction to energy of a closed circular string rotating in S^5. The string is spinning around its center of mass with two equal angular momenta J_2=J_3 and its center of mass angular momentum is J_1. We revise the argument in hep-th/0306130 that the 1-loop correction is suppressed by 1/J factor (J= J_1 + 2 J_2 is the total SO(6) spin) relative to the classical term in the energy and use numerical methods to compute the leading 1-loop coefficient. The corresponding gauge theory result is known (hep-th/0405055) only in the J_1=0 limit when the string solution becomes unstable and thus the 1-loop shift of the energy formally contains an imaginary part. While the comparison with gauge theory may not be well-defined in this case, our numerical string theory value of the 1-loop coefficient seems to disagree with the gauge theory one. A plausible explanation should be (as in hep-th/0405001) in the different order of limits taken on the gauge theory and the string theory sides of the AdS/CFT duality.

On one-loop correction to energy of spinning strings in S^5

TL;DR

This work investigates the one-loop correction to the energy of a circular spinning string in S^5 within AdS/CFT, focusing on the leading 1/J term governed by the coefficient d1 in the semiclassical energy expansion. The authors refine the theoretical treatment of E1, address singularities in fluctuation frequencies, and implement a convergent regularization to extract d1 numerically across a range of q and winding k. Their results reveal nontrivial q–k dependence, including zeros of d1 in the stable region, and indicate a discrepancy with gauge-theory predictions, particularly in the unstable q=1 case. They argue that order-of-limits or wrapping effects may underlie the mismatch, with implications for Bethe Ansatz approaches to the quantum string spectrum and for reconciling string and gauge descriptions in the 1/J regime.

Abstract

We revisit the computation (hep-th/0306130) of 1-loop AdS_5 x S^5 superstring sigma model correction to energy of a closed circular string rotating in S^5. The string is spinning around its center of mass with two equal angular momenta J_2=J_3 and its center of mass angular momentum is J_1. We revise the argument in hep-th/0306130 that the 1-loop correction is suppressed by 1/J factor (J= J_1 + 2 J_2 is the total SO(6) spin) relative to the classical term in the energy and use numerical methods to compute the leading 1-loop coefficient. The corresponding gauge theory result is known (hep-th/0405055) only in the J_1=0 limit when the string solution becomes unstable and thus the 1-loop shift of the energy formally contains an imaginary part. While the comparison with gauge theory may not be well-defined in this case, our numerical string theory value of the 1-loop coefficient seems to disagree with the gauge theory one. A plausible explanation should be (as in hep-th/0405001) in the different order of limits taken on the gauge theory and the string theory sides of the AdS/CFT duality.

Paper Structure

This paper contains 5 sections, 44 equations, 8 figures, 1 table.

Table of Contents

  1. Introduction
  2. Structure of one-loop correction
  3. Structure of one-loop correction
  4. Results of numerical evaluation
  5. Concluding remarks

Figures (8)

  • Figure 1: $q$-dependence of $d_1$ for $\hbox{k}=1$
  • Figure 2: $q$-dependence of $d_1$ for $\hbox{k}=2$
  • Figure 3: $q$-dependence of $d_2$ for $\hbox{k}=2$
  • Figure 4: $q$-dependence of $d_1$ for $\hbox{k}=4$
  • Figure 5: $q$-dependence of $d_1$ for $\hbox{k}=8$
  • ...and 3 more figures