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Non-perturbative equivalences among large N gauge theories with adjoint and bifundamental matter fields

Pavel Kovtun, Mithat Unsal, Laurence G. Yaffe

TL;DR

The paper establishes a non-perturbative large-$N_{ m c}$ equivalence between a parent $U(N_{ m c})$ gauge theory with adjoint matter and its orbifold daughter theories by comparing their loop equations on a lattice. It shows that, in the strong-coupling/large-mass regime and with unbroken orbifold and theory-space symmetries, the loop equations of the parent and daughter theories coincide after an appropriate rescaling of couplings, implying identical predictions for Wilson-loop observables, string tensions, and particle spectra. The authors extend the loop-equation framework to decorated Wilson loops with both scalars and fermions via an extended lattice construction, and demonstrate that the non-perturbative equivalence holds for single-trace and two-loop connected correlators. They discuss how symmetry realizations constrain the mapping and acknowledge limitations to phases with broken symmetries, while outlining potential generalizations to more complex orbifolds and beyond the strong-coupling regime. Overall, the work provides a rigorous, non-perturbative foundation for large-$N_{ m c}$ orbifold equivalences in a broad class of gauge theories, independent of supersymmetry or continuum limits.

Abstract

We prove an equivalence, in the large N limit, between certain U(N) gauge theories containing adjoint representation matter fields and their orbifold projections. Lattice regularization is used to provide a non-perturbative definition of these theories; our proof applies in the strong coupling, large mass phase of the theories. Equivalence is demonstrated by constructing and comparing the loop equations for a parent theory and its orbifold projections. Loop equations for both expectation values of single-trace observables, and for connected correlators of such observables, are considered; hence the demonstrated non-perturbative equivalence applies to the large N limits of both string tensions and particle spectra.

Non-perturbative equivalences among large N gauge theories with adjoint and bifundamental matter fields

TL;DR

The paper establishes a non-perturbative large- equivalence between a parent gauge theory with adjoint matter and its orbifold daughter theories by comparing their loop equations on a lattice. It shows that, in the strong-coupling/large-mass regime and with unbroken orbifold and theory-space symmetries, the loop equations of the parent and daughter theories coincide after an appropriate rescaling of couplings, implying identical predictions for Wilson-loop observables, string tensions, and particle spectra. The authors extend the loop-equation framework to decorated Wilson loops with both scalars and fermions via an extended lattice construction, and demonstrate that the non-perturbative equivalence holds for single-trace and two-loop connected correlators. They discuss how symmetry realizations constrain the mapping and acknowledge limitations to phases with broken symmetries, while outlining potential generalizations to more complex orbifolds and beyond the strong-coupling regime. Overall, the work provides a rigorous, non-perturbative foundation for large- orbifold equivalences in a broad class of gauge theories, independent of supersymmetry or continuum limits.

Abstract

We prove an equivalence, in the large N limit, between certain U(N) gauge theories containing adjoint representation matter fields and their orbifold projections. Lattice regularization is used to provide a non-perturbative definition of these theories; our proof applies in the strong coupling, large mass phase of the theories. Equivalence is demonstrated by constructing and comparing the loop equations for a parent theory and its orbifold projections. Loop equations for both expectation values of single-trace observables, and for connected correlators of such observables, are considered; hence the demonstrated non-perturbative equivalence applies to the large N limits of both string tensions and particle spectra.

Paper Structure

This paper contains 18 sections, 87 equations.

Table of Contents

  1. Introduction
  2. Pure gauge theory
  3. Definitions
  4. Loop equations
  5. Large $\bm N_{\rm c}$ limit, strong-coupling expansion, and uniqueness
  6. Multi-loop connected correlators
  7. Adjoint matter fields
  8. Lattice discretization
  9. Geometric encoding of observables
  10. Loop equations
  11. Multi-loop connected correlators
  12. Orbifold theories
  13. Orbifold projection
  14. Loop equations in daughter orbifold theories
  15. Multi-loop connected correlators
  16. ...and 3 more sections