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Quantum fluctuations of Wilson loops from string models

Y. Kinar, E. Schreiber, J. Sonnenschein, N. Weiss

TL;DR

This work analyzes quadratic quantum fluctuations around classical string configurations describing Wilson loops in gauge/gravity duals. It derives the bosonic fluctuation operators in various gauges, shows that the normal-coordinate gauge is best behaved, and demonstrates a universal Lüscher-type $1/L$ correction in confining backgrounds, with an attractive sign. In the AdS$_5\times$S$^5$ case, fermionic fluctuations partially cancel bosonic contributions, leaving a residual Lüscher-type term whose coefficient is not fixed due to gauge and determinant ambiguities; in pure YM-like confining backgrounds, the result is a clean $-7\pi/(24L)$ correction from seven massless bosonic modes. Overall, the paper clarifies how quantum string fluctuations encode universal short-range corrections to the quark-antiquark potential across different backgrounds, providing a bridge between gauge theory confinement and string-theoretic descriptions.

Abstract

We discuss the impact of quadratic quantum fluctuations on the Wilson loop extracted from classical string theory. We show that a large class of models, which includes the near horizon limit of D_p branes with 16 supersymmetries, admits a Lüscher type correction to the classical potential. We confirm that the quantum determinant associated with a BPS configuration of a single quark in the AdS_5 \times S^5 model is free from divergences. We find that for the Wilson loop in that model, unlike the situation in flat space-time, the fermionic determinant does not cancel the bosonic one. For string models that correspond to gauge theories in the confining phase, we show that the correction to the potential is of a Lüscher type and is attractive.

Quantum fluctuations of Wilson loops from string models

TL;DR

This work analyzes quadratic quantum fluctuations around classical string configurations describing Wilson loops in gauge/gravity duals. It derives the bosonic fluctuation operators in various gauges, shows that the normal-coordinate gauge is best behaved, and demonstrates a universal Lüscher-type correction in confining backgrounds, with an attractive sign. In the AdSS case, fermionic fluctuations partially cancel bosonic contributions, leaving a residual Lüscher-type term whose coefficient is not fixed due to gauge and determinant ambiguities; in pure YM-like confining backgrounds, the result is a clean correction from seven massless bosonic modes. Overall, the paper clarifies how quantum string fluctuations encode universal short-range corrections to the quark-antiquark potential across different backgrounds, providing a bridge between gauge theory confinement and string-theoretic descriptions.

Abstract

We discuss the impact of quadratic quantum fluctuations on the Wilson loop extracted from classical string theory. We show that a large class of models, which includes the near horizon limit of D_p branes with 16 supersymmetries, admits a Lüscher type correction to the classical potential. We confirm that the quantum determinant associated with a BPS configuration of a single quark in the AdS_5 \times S^5 model is free from divergences. We find that for the Wilson loop in that model, unlike the situation in flat space-time, the fermionic determinant does not cancel the bosonic one. For string models that correspond to gauge theories in the confining phase, we show that the correction to the potential is of a Lüscher type and is attractive.

Paper Structure

This paper contains 20 sections, 101 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. The classical setup
  3. Quadratic fluctuations and gauge fixings in the NG action
  4. The fixed $u$ gauge
  5. The normal coordinate gauge
  6. The fixed $x$ gauge
  7. Comparing the different gauges
  8. Bosonic string in flat space-time
  9. A General scaling result
  10. Bosonic string in the $AdS_5\times S^5$ background
  11. The bosonic string in the $AdS_5\times S^5$ background -- Polyakov's action
  12. Introducing fermionic fluctuations
  13. Fermions in flat space-time
  14. Fermions in $AdS_5\times S^5$
  15. Bare quark in $AdS_5\times S^5$
  16. ...and 5 more sections

Figures (3)

  • Figure 1: The fluctuations in the normal gauge
  • Figure 2: A problematic fluctuation in the fixed $u$ gauge
  • Figure 3: (a) The classical solution is rescaled as $L \rightarrow \infty$ in the $AdS_5\times S^5$ background while (b) It becomes flatter in the confining scenario