# Light-front holographic QCD and emerging confinement

## Abstract

In this study we explore the remarkable connections between light-front dynamics, its holographic mapping to gravity in a higher-dimensional anti-de Sitter (AdS) space, and conformal quantum mechanics. This approach provides new insights into the origin of a fundamental mass scale and the physics underlying confinement dynamics in QCD in the limit of massless quarks. The result is a relativistic light-front wave equation for arbitrary spin with an effective confinement potential derived from a conformal action and its embedding in AdS space. This equation allows for the computation of essential features of hadron spectra in terms of a single scale. The light-front holographic methods described here give a precise interpretation of holographic variables and quantities in AdS space in terms of light-front variables and quantum numbers. This leads to a relation between the AdS wave functions and the boost-invariant light-front wave functions describing the internal structure of hadronic bound-states in physical spacetime. The pion is massless in the chiral limit and the excitation spectra of relativistic light-quark meson and baryon bound states lie on linear Regge trajectories with identical slopes in the radial and orbital quantum numbers. In the light-front holographic approach described here currents are expressed as an infinite summore »

- Authors:

- SLAC National Accelerator Lab., Menlo Park, CA (United States)
- Univ. of Costa Rica, San Pedro (Costa Rica)
- Institut fur Theoretische Physik, Heidelberg (Germany)
- College of William and Mary, Williamsburg, VA (United States)

- Publication Date:

- Research Org.:
- SLAC National Accelerator Lab., Menlo Park, CA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)

- OSTI Identifier:
- 1149335

- Alternate Identifier(s):
- OSTI ID: 1359752

- Report Number(s):
- SLAC-PUB-15972

Journal ID: ISSN 0370-1573; PII: S0370157315002306

- Grant/Contract Number:
- AC02-76SF00515; PHY1068008; PHY-1068008

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Physics Reports

- Additional Journal Information:
- Journal Volume: 584; Journal Issue: C; Journal ID: ISSN 0370-1573

- Publisher:
- Elsevier

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; phenomenology-HEP; theory-HEP; HEPPH; HEPTH

### Citation Formats

```
Brodsky, Stanley J., de Téramond, Guy F., Dosch, Hans Günter, and Erlich, Joshua. Light-front holographic QCD and emerging confinement. United States: N. p., 2015.
Web. doi:10.1016/j.physrep.2015.05.001.
```

```
Brodsky, Stanley J., de Téramond, Guy F., Dosch, Hans Günter, & Erlich, Joshua. Light-front holographic QCD and emerging confinement. United States. doi:10.1016/j.physrep.2015.05.001.
```

```
Brodsky, Stanley J., de Téramond, Guy F., Dosch, Hans Günter, and Erlich, Joshua. Thu .
"Light-front holographic QCD and emerging confinement". United States. doi:10.1016/j.physrep.2015.05.001. https://www.osti.gov/servlets/purl/1149335.
```

```
@article{osti_1149335,
```

title = {Light-front holographic QCD and emerging confinement},

author = {Brodsky, Stanley J. and de Téramond, Guy F. and Dosch, Hans Günter and Erlich, Joshua},

abstractNote = {In this study we explore the remarkable connections between light-front dynamics, its holographic mapping to gravity in a higher-dimensional anti-de Sitter (AdS) space, and conformal quantum mechanics. This approach provides new insights into the origin of a fundamental mass scale and the physics underlying confinement dynamics in QCD in the limit of massless quarks. The result is a relativistic light-front wave equation for arbitrary spin with an effective confinement potential derived from a conformal action and its embedding in AdS space. This equation allows for the computation of essential features of hadron spectra in terms of a single scale. The light-front holographic methods described here give a precise interpretation of holographic variables and quantities in AdS space in terms of light-front variables and quantum numbers. This leads to a relation between the AdS wave functions and the boost-invariant light-front wave functions describing the internal structure of hadronic bound-states in physical spacetime. The pion is massless in the chiral limit and the excitation spectra of relativistic light-quark meson and baryon bound states lie on linear Regge trajectories with identical slopes in the radial and orbital quantum numbers. In the light-front holographic approach described here currents are expressed as an infinite sum of poles, and form factors as a product of poles. At large q2 the form factor incorporates the correct power-law fall-off for hard scattering independent of the specific dynamics and is dictated by the twist. At low q2 the form factor leads to vector dominance. The approach is also extended to include small quark masses. We briefly review in this report other holographic approaches to QCD, in particular top-down and bottom-up models based on chiral symmetry breaking. We also include a discussion of open problems and future applications.},

doi = {10.1016/j.physrep.2015.05.001},

journal = {Physics Reports},

number = C,

volume = 584,

place = {United States},

year = {2015},

month = {5}

}

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Works referencing / citing this record:

##
Schwinger’s proper time and worldline holographic renormalization

journal, April 2017

- Dietrich, Dennis D.; Koenigstein, Adrian
- Physical Review D, Vol. 95, Issue 7

##
Fermions in worldline holography

journal, September 2017

- Dietrich, Dennis D.; Koenigstein, Adrian
- Physical Review D, Vol. 96, Issue 5