TY - JOUR

T1 - 1/2-BPS vortex strings in N = 2 supersymmetric U(1)N gauge theories

AU - Gudnason, Sven Bjarke

AU - Eto, Minoru

AU - Nitta, Muneto

N1 - Funding Information:
S.B.G. thanks Xiaosen Han, Keisuke Ohashi, Calum Ross, and Yisong Yang for discussions and correspondence. S.B.G. thanks the Outstanding Talent Program of Henan University for partial support. S.B.G. was supported by the National Natural Science Foundation of China (Grant Nos. 11675223 and 12071111). M.E. was supported, in part, by the JSPS Grant-in-Aid for Scientific Research (KAKENHI Grant No.
Funding Information:
JP19K03839) and also by MEXT KAKENHI Grant-in-Aid for Scientific Research on Innovative Areas, Discrete Geometric Analysis for Materials Design, Grant No. JP17H06462 from the MEXT of Japan. M.N. was supported, in part, by the JSPS Grant-in-Aid for Scientific Research (KAKENHI Grant No. 18H01217).
Publisher Copyright:
© 2021 Author(s).
Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2021/3/1

Y1 - 2021/3/1

N2 - Strings in N=2 supersymmetric U(1)N gauge theories with N hypermultiplets are studied in the generic setting of an arbitrary Fayet-Iliopoulos triplet of parameters for each gauge group and an invertible charge matrix. Although the string tension is generically of a square-root form, it turns out that all existing Bogomol'nyi-Prasad-Sommerfield solutions have a tension that is linear in the magnetic fluxes, which, in turn, are linearly related to the winding numbers. The main result is a series of theorems establishing three different kinds of solutions of the so-called constraint equations, which can be pictured as orthogonal directions to the magnetic flux in SU(2)R space. We further prove for all cases that a seemingly vanishing Bogomol'nyi bound cannot have solutions. Finally, we write down the most general vortex equations in both master form and Taubes-like form. Remarkably, the final vortex equations essentially look Abelian in the sense that there is no trace of the SU(2)R symmetry in the equations after the constraint equations have been solved.

AB - Strings in N=2 supersymmetric U(1)N gauge theories with N hypermultiplets are studied in the generic setting of an arbitrary Fayet-Iliopoulos triplet of parameters for each gauge group and an invertible charge matrix. Although the string tension is generically of a square-root form, it turns out that all existing Bogomol'nyi-Prasad-Sommerfield solutions have a tension that is linear in the magnetic fluxes, which, in turn, are linearly related to the winding numbers. The main result is a series of theorems establishing three different kinds of solutions of the so-called constraint equations, which can be pictured as orthogonal directions to the magnetic flux in SU(2)R space. We further prove for all cases that a seemingly vanishing Bogomol'nyi bound cannot have solutions. Finally, we write down the most general vortex equations in both master form and Taubes-like form. Remarkably, the final vortex equations essentially look Abelian in the sense that there is no trace of the SU(2)R symmetry in the equations after the constraint equations have been solved.

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U2 - 10.1063/5.0039068

DO - 10.1063/5.0039068

M3 - Article

AN - SCOPUS:85102457381

VL - 62

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 3

M1 - 032304

ER -