New constraint on effective field theories of the QCD flux tube
Abstract
Effective magnetic S U (N ) gauge theory with classical ZN flux tubes of intrinsic width 1/M is an effective field theory of the long-distance quark-antiquark interaction in S U (N ) Yang-Mills theory. Long-wavelength fluctuations of the ZN vortices of this theory lead to an effective string theory. In this paper, we clarify the connection between effective field theory and effective string theory, and we propose a new constraint on these vortices. We first examine the impact of string fluctuations on the classical dual superconductor description of confinement. At interquark distances R ∼1/M , the classical action for a straight flux tube determines the heavy quark potentials. At distances R ≫1/M , fluctuations of the flux tube axis x ∼ give rise to an effective string theory with an action Seff(x ∼), the classical action for a curved flux tube, evaluated in the limit 1/M →0 . This action is equal to the Nambu-Goto action. These conclusions are independent of the details of the ZN flux tube. Further, we assume the QCD flux tube satisfies the additional constraint, ∫0∞r d r T/θθ(r ) r2=0 , where T/θθ(r ) r2 is the value of the θ θ component of the stress tensor at a distance r from the axis of an infinite flux tube. Under this constraint, the string tension σ equals the force on a quark in the chromoelectric field E → of an infinite straight flux tube, and the Nambu-Goto action can be represented in terms of the chromodynamic fields of effective magnetic S U (N ) gauge theory, yielding a field theory interpretation of effective string theory.
- Publication:
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Physical Review D
- Pub Date:
- March 2016
- DOI:
- 10.1103/PhysRevD.93.054012
- arXiv:
- arXiv:1512.02705
- Bibcode:
- 2016PhRvD..93e4012B
- Keywords:
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- High Energy Physics - Phenomenology;
- High Energy Physics - Lattice;
- High Energy Physics - Theory
- E-Print:
- 29 pages, 3 figures, fixed typos and references