# Hopf Skyrmion in QCD with adjoint quarks

## Abstract

We consider a modification of QCD in which conventional fundamental quarks are replaced by Weyl fermions in the adjoint representation of the color SU(N). In the case of two flavors the low-energy chiral Lagrangian is that of the Skyrme-Faddeev model. The latter supports topologically stable solitons with mass scaling as N{sup 2}. Topological stability is due to the existence of a nontrivial Hopf invariant in the Skyrme-Faddeev model. Our task is to identify, at the level of the fundamental theory, adjoint QCD, an underlying reason responsible for the stability of the corresponding hadrons. We argue that all 'normal' mesons and baryons, with mass O(N{sup 0}), are characterized by (-1){sup Q}(-1){sup F}=1, where Q is a conserved charge corresponding to the unbroken U(1) surviving in the process of the chiral symmetry breaking (SU(2){yields}U(1) for two adjoint flavors). Moreover, F is the fermion number (defined mod 2 in the case at hand). We argue that there exist exotic hadrons with mass O(N{sup 2}) and (-1){sup Q}(-1){sup F}=-1. They are in one-to-one correspondence with the Hopf Skyrmions. The transition from nonexotic to exotic hadrons is due to a shift in F, namely F{yields}F-H where H is the Hopf invariant. To detect this phenomenonmore »

- Authors:

- Niels Bohr Institute, Blegdamsvej 17, DK-2100 Copenhagen O (Denmark)
- William I. Fine Theoretical Physics Institute, University of Minnesota, 116 Church St. S.E., Minneapolis, Minnesota 55455 (United States)

- Publication Date:

- OSTI Identifier:
- 21020199

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 6; Other Information: DOI: 10.1103/PhysRevD.75.065020; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; BARYONS; CHIRAL SYMMETRY; CHIRALITY; COLOR MODEL; FLAVOR MODEL; LAGRANGIAN FUNCTION; MESONS; QUANTUM CHROMODYNAMICS; QUARKS; SKYRME POTENTIAL; SOLITONS; SU GROUPS; SYMMETRY BREAKING; TOPOLOGY

### Citation Formats

```
Bolognesi, S., and Shifman, M.
```*Hopf Skyrmion in QCD with adjoint quarks*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVD.75.065020.

```
Bolognesi, S., & Shifman, M.
```*Hopf Skyrmion in QCD with adjoint quarks*. United States. doi:10.1103/PHYSREVD.75.065020.

```
Bolognesi, S., and Shifman, M. Thu .
"Hopf Skyrmion in QCD with adjoint quarks". United States.
doi:10.1103/PHYSREVD.75.065020.
```

```
@article{osti_21020199,
```

title = {Hopf Skyrmion in QCD with adjoint quarks},

author = {Bolognesi, S. and Shifman, M.},

abstractNote = {We consider a modification of QCD in which conventional fundamental quarks are replaced by Weyl fermions in the adjoint representation of the color SU(N). In the case of two flavors the low-energy chiral Lagrangian is that of the Skyrme-Faddeev model. The latter supports topologically stable solitons with mass scaling as N{sup 2}. Topological stability is due to the existence of a nontrivial Hopf invariant in the Skyrme-Faddeev model. Our task is to identify, at the level of the fundamental theory, adjoint QCD, an underlying reason responsible for the stability of the corresponding hadrons. We argue that all 'normal' mesons and baryons, with mass O(N{sup 0}), are characterized by (-1){sup Q}(-1){sup F}=1, where Q is a conserved charge corresponding to the unbroken U(1) surviving in the process of the chiral symmetry breaking (SU(2){yields}U(1) for two adjoint flavors). Moreover, F is the fermion number (defined mod 2 in the case at hand). We argue that there exist exotic hadrons with mass O(N{sup 2}) and (-1){sup Q}(-1){sup F}=-1. They are in one-to-one correspondence with the Hopf Skyrmions. The transition from nonexotic to exotic hadrons is due to a shift in F, namely F{yields}F-H where H is the Hopf invariant. To detect this phenomenon we have to extend the Skyrme-Faddeev model by introducing fermions.},

doi = {10.1103/PHYSREVD.75.065020},

journal = {Physical Review. D, Particles Fields},

number = 6,

volume = 75,

place = {United States},

year = {Thu Mar 15 00:00:00 EDT 2007},

month = {Thu Mar 15 00:00:00 EDT 2007}

}