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A Soluble String Theory of Hadrons

Eric G. Gimon, Leopoldo A. Pando Zayas, Jacob Sonnenschein, Matthew J. Strassler

TL;DR

This work studies Penrose limits of the Maldacena-Núñez and Klebanov-Strassler backgrounds to produce exactly solvable plane-wave string theories that capture the IR physics of confining N=1 gauge theories. The authors interpret the resulting string spectrum as heavy, nonrelativistic hadrons called annulons, with mass $M_0=m_0J$ and low-energy excitations organized by a universal $v$-sector and a model-dependent internal sector. A simple toy model of a string boosted along a compact circle reproduces key spectral features and motivates the annulon picture, while a Wilson loop calculation with large charge reveals confinement effects that scale quadratically with the string tension. The framework yields a coherent, soluble holographic description of charged hadrons, with explicit supersymmetry and symmetry considerations guiding constituent insertions and multiplet structure. This approach provides a tractable bridge between the gauge theory IR dynamics and a solvable string theory description of heavy hadrons in confining backgrounds.

Abstract

We consider Penrose limits of the Klebanov-Strassler and Maldacena-Nunez holographic duals to N =1 supersymmetric Yang-Mills. By focusing in on the IR region we obtain exactly solvable string theory models. These represent the nonrelativistic motion and low-lying excitations of heavy hadrons with mass proportional to a large global charge. We argue that these hadrons, both physically and mathematically, take the form of heavy nonrelativistic strings; we term them "annulons." A simple toy model of a string boosted along a compact circle allows us considerable insight into their properties. We also calculate the Wilson loop carrying large global charge and show the effect of confinement is quadratic, not linear, in the string tension.

A Soluble String Theory of Hadrons

TL;DR

This work studies Penrose limits of the Maldacena-Núñez and Klebanov-Strassler backgrounds to produce exactly solvable plane-wave string theories that capture the IR physics of confining N=1 gauge theories. The authors interpret the resulting string spectrum as heavy, nonrelativistic hadrons called annulons, with mass and low-energy excitations organized by a universal -sector and a model-dependent internal sector. A simple toy model of a string boosted along a compact circle reproduces key spectral features and motivates the annulon picture, while a Wilson loop calculation with large charge reveals confinement effects that scale quadratically with the string tension. The framework yields a coherent, soluble holographic description of charged hadrons, with explicit supersymmetry and symmetry considerations guiding constituent insertions and multiplet structure. This approach provides a tractable bridge between the gauge theory IR dynamics and a solvable string theory description of heavy hadrons in confining backgrounds.

Abstract

We consider Penrose limits of the Klebanov-Strassler and Maldacena-Nunez holographic duals to N =1 supersymmetric Yang-Mills. By focusing in on the IR region we obtain exactly solvable string theory models. These represent the nonrelativistic motion and low-lying excitations of heavy hadrons with mass proportional to a large global charge. We argue that these hadrons, both physically and mathematically, take the form of heavy nonrelativistic strings; we term them "annulons." A simple toy model of a string boosted along a compact circle allows us considerable insight into their properties. We also calculate the Wilson loop carrying large global charge and show the effect of confinement is quadratic, not linear, in the string tension.

Paper Structure

This paper contains 31 sections, 151 equations, 1 figure.

Table of Contents

  1. Introduction and Summary
  2. Null geodesics in the IR of confining theories
  3. The Maldacena-Núñez background
  4. The Penrose limit
  5. The Klebanov-Strassler background
  6. A convenient parameterization of the KS background
  7. Plane wave limit
  8. The various forms in the plane wave limit
  9. Operators and symmetries
  10. The plane wave string and its Hamiltonian
  11. Bosonic Sector
  12. The fermionic sector
  13. A string theory of hadrons
  14. The toy model of a string on a compact circle
  15. The hadrons in the KS case
  16. ...and 16 more sections

Figures (1)

  • Figure 1: In the string dual of a confining theory, the quark and antiquark sources are given by the $r$-dependent segments near the ends of the string, while the flux tube between them is given by the region of the string lying at $r=r_0$.