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Multiply wound Polyakov loops at strong coupling

Sean A. Hartnoll, S. Prem Kumar

TL;DR

This paper analyzes the strong-coupling behavior of multiply wound Polyakov-Maldacena loops in ${\mathcal N}=4$ SYM via holographic duals. It shows that D3-brane probes collapse to the cigar and do not generate nontrivial $k$-dependence, while D5-brane probes with flux yield $k/N$-dependent corrections and reveal an emergent $N^{-2/3}$ scaling near a Gross-Witten-like regime. The results identify the correct bulk degrees of freedom for these observables and uncover intriguing nonanalytic corrections, highlighting a connection between bulk brane dynamics and phase-transition-like behavior in the gauge theory. The findings motivate further exploration of double-scaling limits and the field-theory interpretation of D5 configurations, with potential implications for the finite-temperature phase structure of the theory.

Abstract

We study the expectation value of a Polyakov-Maldacena loop that wraps the thermal circle k times in strongly coupled N=4 super Yang-Mills theory. This is achieved by considering probe D3 and D5 brane embeddings in the dual black hole geometry. In contrast to multiply wound spatial Wilson loops, nontrivial dependence on k is captured through D5 branes. We find N^{-2/3} corrections, reminiscent of the scaling behaviour near a Gross-Witten transition.

Multiply wound Polyakov loops at strong coupling

TL;DR

This paper analyzes the strong-coupling behavior of multiply wound Polyakov-Maldacena loops in SYM via holographic duals. It shows that D3-brane probes collapse to the cigar and do not generate nontrivial -dependence, while D5-brane probes with flux yield -dependent corrections and reveal an emergent scaling near a Gross-Witten-like regime. The results identify the correct bulk degrees of freedom for these observables and uncover intriguing nonanalytic corrections, highlighting a connection between bulk brane dynamics and phase-transition-like behavior in the gauge theory. The findings motivate further exploration of double-scaling limits and the field-theory interpretation of D5 configurations, with potential implications for the finite-temperature phase structure of the theory.

Abstract

We study the expectation value of a Polyakov-Maldacena loop that wraps the thermal circle k times in strongly coupled N=4 super Yang-Mills theory. This is achieved by considering probe D3 and D5 brane embeddings in the dual black hole geometry. In contrast to multiply wound spatial Wilson loops, nontrivial dependence on k is captured through D5 branes. We find N^{-2/3} corrections, reminiscent of the scaling behaviour near a Gross-Witten transition.

Paper Structure

This paper contains 17 sections, 55 equations, 4 figures, 1 table.

Table of Contents

  1. Motivation and Introduction
  2. Phase structure of ${\mathcal{N}}=4$ SYM theory
  3. Multiply wound Polyakov-Maldacena loops
  4. (No) D3 brane solutions
  5. Equations of motion
  6. Boundary terms and boundary conditions
  7. Solving the equations
  8. The solutions at large $\kappa$
  9. Continuity as a function of $\kappa$ and boundary conditions
  10. The minimum radius as a function of boundary conditions
  11. Implications of the D3 brane results
  12. D5 brane solutions
  13. Equations of motion
  14. Boundary terms and action
  15. Constant solutions
  16. ...and 2 more sections

Figures (4)

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