Abstract
We study spectrum of D = 2 \(\mathcal {N} \) = (2, 2) QED with N + 1 massive charged chiral multiplets, with care given to precise supermultiplet countings. In the infrared the theory flows to ℂℙN model with twisted masses, where we construct generic flavored kink solitons for the large mass regime, and study their quantum degeneracies. These kinks are qualitatively different and far more numerous than those of small mass regime, with features reminiscent of multi-pronged (p, q) string web, complete with the wall-crossing behavior. It has been also conjectured that spectrum of this theory is equivalent to the hypermultiplet spectrum of a certain D = 4 Seiberg-Witten theory. We find that the correspondence actually extends beyond hypermultiplets in D = 4, and that many of the relevant indices match. However, a D = 2 BPS state is typically mapped to several different kind of dyons whose individual supermultiplets are rather complicated; the match of index comes about only after summing over indices of these different dyons. We note general wall-crossing behavior of flavored BPS kink states, and compare it to those of D = 4 dyons.
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References
N. Seiberg and E. Witten, Monopole condensation, and confinement in N = 2 supersymmetric Yang-Mills theory, Nucl. Phys. B 426 (1994) 19 [Erratum ibid. B 430 (1994) 485] [hep-th/9407087] [SPIRES].
F. Ferrari and A. Bilal, The strong-coupling spectrum of the Seiberg-Witten theory, Nucl. Phys. B 469 (1996) 387 [hep-th/9602082] [SPIRES].
A. Bilal and F. Ferrari, Curves of marginal stability and weak and Strong-Coupling BPS spectra in N = 2 supersymmetric QCD, Nucl. Phys. B 480 (1996) 589 [hep-th/9605101] [SPIRES].
E.J. Weinberg and P. Yi, Magnetic monopole dynamics, supersymmetry and duality, Phys. Rept. 438 (2007) 65 [hep-th/0609055] [SPIRES].
A. Mikhailov, N. Nekrasov and S. Sethi, Geometric realizations of BPS states in N = 2 theories, Nucl. Phys. B 531 (1998) 345 [hep-th/9803142] [SPIRES].
O. Bergman, Three-pronged strings and 1/4 BPS states in N = 4 super-Yang-Mills theory, Nucl. Phys. B 525 (1998) 104 [hep-th/9712211] [SPIRES].
K.-M. Lee and P. Yi, Dyons in N = 4 supersymmetric theories and three-pronged strings, Phys. Rev. D 58 (1998) 066005 [hep-th/9804174] [SPIRES].
D. Bak, C.-k. Lee, K.-M. Lee and P. Yi, Low energy dynamics for 1/4 BPS dyons, Phys. Rev. D 61 (2000) 025001 [hep-th/9906119] [SPIRES].
D. Bak, K.-M. Lee and P. Yi, Quantum 1/4 BPS dyons, Phys. Rev. D 61 (2000) 045003 [hep-th/9907090] [SPIRES].
J.P. Gauntlett, N. Kim, J. Park and P. Yi, Monopole dynamics and BPS dyons in N = 2 super-Yang-Mills theories, Phys. Rev. D 61 (2000) 125012 [hep-th/9912082] [SPIRES].
A. Ritz, M.A. Shifman, A.I. Vainshtein and M.B. Voloshin, Marginal stability and the metamorphosis of BPS states, Phys. Rev. D 63 (2001) 065018 [hep-th/0006028] [SPIRES].
P.C. Argyres and K. Narayan, String webs from field theory, JHEP 03 (2001) 047 [hep-th/0101114] [SPIRES].
F. Denef, Supergravity flows and D-brane stability, JHEP 08 (2000) 050 [hep-th/0005049] [SPIRES].
D. Gaiotto, G.W. Moore and A. Neitzke, Four-dimensional wall-crossing via three-dimensional field theory, arXiv:0807.4723 [SPIRES].
D. Gaiotto, G.W. Moore and A. Neitzke, Wall-crossing, Hitchin Systems and the WKB Approximation, arXiv:0907.3987 [SPIRES].
M. Kontsevich and Y. Soibelman, Stability structures, motivic Donaldson-Thomas invariants and cluster transformations, math.AG/0811.2435.
S. Cecotti and C. Vafa, BPS Wall Crossing and topological strings, arXiv:0910.2615 [SPIRES].
T. Dimofte and S. Gukov, Refined, motivic and quantum, Lett. Math. Phys. 91 (2010) 1 [arXiv:0904.1420] [SPIRES].
M. Stern and P. Yi, Counting Yang-Mills dyons with index theorems, Phys. Rev. D 62 (2000) 125006 [hep-th/0005275] [SPIRES].
F. Denef, Quantum quivers and Hall/hole halos, JHEP 10 (2002) 023 [hep-th/0206072] [SPIRES].
S. Cecotti, P. Fendley, K.A. Intriligator and C. Vafa, A new supersymmetric index, Nucl. Phys. B 386 (1992) 405 [hep-th/9204102] [SPIRES].
S. Cecotti and C. Vafa, On classification of N = 2 supersymmetric theories, Commun. Math. Phys. 158 (1993) 569 [hep-th/9211097] [SPIRES].
S. Cecotti and C. Vafa, Topological antitopological fusion, Nucl. Phys. B 367 (1991) 359 [SPIRES].
N. Dorey, The BPS spectra of two-dimensional supersymmetric gauge theories with twisted mass terms, JHEP 11 (1998) 005 [hep-th/9806056] [SPIRES].
N. Dorey, T.J. Hollowood and D. Tong, The BPS spectra of gauge theories in two and four dimensions, JHEP 05 (1999) 006 [hep-th/9902134] [SPIRES].
A. Hanany and K. Hori, Branes and N = 2 theories in two dimensions, Nucl. Phys. B 513 (1998) 119 [hep-th/9707192] [SPIRES].
A. Hanany and D. Tong, Vortex strings and four-dimensional gauge dynamics, JHEP 04 (2004) 066 [hep-th/0403158] [SPIRES].
M. Shifman and A. Yung, Non-Abelian string junctions as confined monopoles, Phys. Rev. D 70 (2004) 045004 [hep-th/0403149] [SPIRES].
D. Tong, TASI lectures on solitons, hep-th/0509216 [SPIRES].
M. Shifman and A. Yung, Supersymmetric solitons and how they help us understand non-Abelian gauge theories, Rev. Mod. Phys. 79 (2007) 1139 [hep-th/0703267] [SPIRES].
D. Tong, Quantum vortex strings: a review, Annals Phys. 324 (2009) 30 [arXiv:0809.5060] [SPIRES].
M. Shifman, A. Vainshtein and R. Zwicky, Central charge anomalies in 2D σ-models with twisted mass, J. Phys. A 39 (2006) 13005 [hep-th/0602004] [SPIRES].
S. Olmez and M. Shifman, Curves of marginal stability in two-dimensional CP(N-1) models with Z N -symmetric twisted masses, J. Phys. A 40 (2007) 11151 [hep-th/0703149] [SPIRES].
D. Tong, The moduli space of BPS domain walls, Phys. Rev. D 66 (2002) 025013 [hep-th/0202012] [SPIRES].
L. Álvarez-Gaumé and D.Z. Freedman, Kähler geometry and the renormalization of supersymmetric σ-models, Phys. Rev. D 22 (1980) 846 [SPIRES].
J.P. Gauntlett, C.-j. Kim, K.-M. Lee and P. Yi, General low energy dynamics of supersymmetric monopoles, Phys. Rev. D 63 (2001) 065020 [hep-th/0008031] [SPIRES].
F. Denef and G.W. Moore, Split states, entropy enigmas, holes and halos, hep-th/0702146 [SPIRES].
D. Gaiotto, Surface operators in N = 2 4D gauge theories, arXiv:0911.1316 [SPIRES].
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ArXiv ePrint: 0911.4726
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Lee, S., Yi, P. A study of Wall-Crossing: flavored kinks in D = 2 QED. J. High Energ. Phys. 2010, 55 (2010). https://doi.org/10.1007/JHEP03(2010)055
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DOI: https://doi.org/10.1007/JHEP03(2010)055