Related Experiment Video
Updated: Mar 15, 2026
07:46
Setting Limits on Supersymmetry Using Simplified Models
Published on: November 15, 2013
9.0K
Chiral Lagrangian from Duality and Monopole Operators in Compactified QCD
Aleksey Cherman1, Thomas Schäfer2, Mithat Ünsal2
1Institute for Nuclear Theory, University of Washington, Seattle, Washington 98105 USA.
Physical Review Letters
|September 3, 2016
Summary
We demonstrate a calculable chiral symmetry breaking in Quantum Chromodynamics (QCD) on R³×S¹. This study derives the chiral Lagrangian and condensate, revealing insights into quark masses and Nambu-Goldstone pions.
Area of Science:
- High-energy physics
- Quantum Chromodynamics (QCD)
- Condensed matter theory
Background:
- Quantum Chromodynamics (QCD) describes the strong nuclear force.
- Understanding chiral symmetry breaking is crucial for low-energy QCD.
- Compactification of theories on manifolds like S¹ offers new analytical tools.
Purpose of the Study:
- To investigate chiral symmetry breaking in a specific compactification of QCD.
- To derive key parameters like the chiral Lagrangian and condensate microscopically.
- To explore connections between supersymmetric and non-supersymmetric gauge theories.
Main Methods:
- Compactification of QCD on R³×S¹ with flavor-twisted boundary conditions.
- Utilizing Abelian duality and monopole operators.
- Microscopic derivation of the chiral Lagrangian and condensate.
Main Results:
- Analytical calculation of continuous chiral symmetry breaking in a specific QCD domain.
- Microscopic derivation of the Gell-Mann-Oakes-Renner relation.
- Identification of fractional jumping of fermion zero modes and color-flavor transmutation for Nambu-Goldstone pions.
- Microscopic understanding of constituent quark masses.
Conclusions:
- Results support adiabatic continuity between small and large S¹ regimes.
- Provides concrete microscopic links between N=1, N=2 supersymmetric gauge theories and non-supersymmetric QCD.
- Confirms the role of monopole-instanton operators in inducing chiral symmetry breaking.
Related Concept Videos
01:17Differential Form of Maxwell's Equations
1.4K
James Clerk Maxwell (1831–1879) was one of the significant contributors to physics in the nineteenth century. He is probably best known for having combined existing knowledge of the laws of electricity and the laws of magnetism with his insights to form a complete overarching electromagnetic theory, represented by Maxwell's equations. The four basic laws of electricity and magnetism were discovered experimentally through the work of physicists such as Oersted, Coulomb, Gauss, and...
1.4K
01:28Symmetry in Maxwell's Equations
4.4K
Once the fields have been calculated using Maxwell's four equations, the Lorentz force equation gives the force that the fields exert on a charged particle moving with a certain velocity. The Lorentz force equation combines the force of the electric field and of the magnetic field on the moving charge. Maxwell's equations and the Lorentz force law together encompass all the laws of electricity and magnetism. The symmetry that Maxwell introduced into his mathematical framework may not be...
4.4K
01:30Electric Dipoles and Dipole Moment
6.9K
Consider two charges of equal magnitude but opposite signs. If they cannot be separated by an external electric field, the system is called a permanent dipole. For example, the water molecule is a dipole, making it a good solvent.
Theoretically, studying electric dipoles leads to understanding why the resultant electric forces around us are weak. Since electric forces are strong, remnant net charges are rare. Hence, the interaction between dipoles helps us understand electrical interactions in...
Theoretically, studying electric dipoles leads to understanding why the resultant electric forces around us are weak. Since electric forces are strong, remnant net charges are rare. Hence, the interaction between dipoles helps us understand electrical interactions in...
6.9K
01:25Divergence and Curl of Electric Field
7.5K
The divergence of a vector is a measure of how much the vector spreads out (diverges) from a point. For example, an electric field vector diverges from the positive charge and converges at the negative charge. The divergence of an electric field is derived using Gauss's law and is equal to the charge density divided by the permittivity of space. Mathematically, it is expressed as
7.5K
01:22Second Derivatives and Laplace Operator
2.7K
The first order operators using the del operator include the gradient, divergence and curl. Certain combinations of first order operators on a scalar or vector function yield second order expressions. Second-order expressions play a very important role in mathematics and physics. Some second order expressions include the divergence and curl of a gradient function, the divergence and curl of a curl function, and the gradient of a divergence function.
Consider a scalar function. The curl of its...
Consider a scalar function. The curl of its...
2.7K
02:25Chirality
31.7K
Chirality is a term that describes the lack of mirror symmetry in an object. In other words, chiral objects cannot be superposed on their mirror images. For example, our feet are chiral, as the mirror image of the left foot, the right foot, cannot be superposed on the left foot.
Chiral objects exhibit a sense of handedness when they interact with another chiral object. For example, our left foot can only fit in the left shoe and not in the right shoe. Achiral objects — objects that have...
Chiral objects exhibit a sense of handedness when they interact with another chiral object. For example, our left foot can only fit in the left shoe and not in the right shoe. Achiral objects — objects that have...
31.7K