TY - JOUR

T1 - Effective world-sheet theory for non-Abelian semilocal strings in N=2 supersymmetric QCD

AU - Shifman, M.

AU - Vinci, W.

AU - Yung, A.

PY - 2011/6/10

Y1 - 2011/6/10

N2 - We consider non-Abelian semilocal strings (vortices or vortex strings) arising in N=2 supersymmetric U(N) gauge theory with Nf=N+N∼ matter hypermultiplets in the fundamental representation (quarks) and a Fayet-Iliopoulos term ξ. We present, for the first time ever, a systematic field-theoretic derivation of the world-sheet theory for such strings, describing dynamics of both orientational and size-zero modes. Our derivation is complete in the limit (ln L)→, where L is an infrared regulator in the transverse plane. In this limit, the world-sheet theory is obtained exactly. It is presented by a so-far unknown N=2 two-dimensional sigma model, to which we refer as the zn model, with or without twisted masses. Alternative formulations of the zn model are worked out: conventional and extended gauged formulations and a geometric formulation. We compare the exact metric of the zn model with that of the weighted CP(Nf-1) model conjectured by Hanany and Tong, through D branes, as the world-sheet theory for the non-Abelian semilocal strings. The Hanany-Tong setup has no parallel for the field-theoretic infrared parameter, and metrics of the weighted CP(Nf-1) model and zn model are different. Still, their quasiclassical excitation spectra coincide.

AB - We consider non-Abelian semilocal strings (vortices or vortex strings) arising in N=2 supersymmetric U(N) gauge theory with Nf=N+N∼ matter hypermultiplets in the fundamental representation (quarks) and a Fayet-Iliopoulos term ξ. We present, for the first time ever, a systematic field-theoretic derivation of the world-sheet theory for such strings, describing dynamics of both orientational and size-zero modes. Our derivation is complete in the limit (ln L)→, where L is an infrared regulator in the transverse plane. In this limit, the world-sheet theory is obtained exactly. It is presented by a so-far unknown N=2 two-dimensional sigma model, to which we refer as the zn model, with or without twisted masses. Alternative formulations of the zn model are worked out: conventional and extended gauged formulations and a geometric formulation. We compare the exact metric of the zn model with that of the weighted CP(Nf-1) model conjectured by Hanany and Tong, through D branes, as the world-sheet theory for the non-Abelian semilocal strings. The Hanany-Tong setup has no parallel for the field-theoretic infrared parameter, and metrics of the weighted CP(Nf-1) model and zn model are different. Still, their quasiclassical excitation spectra coincide.

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U2 - 10.1103/PhysRevD.83.125017

DO - 10.1103/PhysRevD.83.125017

M3 - Article

AN - SCOPUS:79960824732

VL - 83

JO - Physical Review D - Particles, Fields, Gravitation and Cosmology

JF - Physical Review D - Particles, Fields, Gravitation and Cosmology

SN - 1550-7998

IS - 12

M1 - 125017

ER -