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Fundamental Vortices, Wall-Crossing, and Particle-Vortex Duality · Around

2017

Fundamental Vortices, Wall-Crossing, and Particle-Vortex Duality

Hwang, Chiung, Yi, Piljin, Yoshida, Yutaka

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We explore 1d vortex dynamics of 3d supersymmetric Yang-Mills theories, as inferred from factorization of exact partition functions.

Under Seiberg-like dualities, the 3d partition function must remain invariant, yet it is not a priori clear what should happen to the vortex dynamics.
We observe that the 1d quivers for the vortices remain the same, and the net effect of the 3d duality map manifests as 1d Wall-Crossing phenomenon; Although the vortex number can shift along such duality maps, the ranks of the 1d quiver theory are unaffected, leading to a notion of fundamental vortices as basic building blocks for topological sectors.
For Aharony-type duality, in particular, where one must supply extra chiral fields to couple with monopole operators on the dual side, 1d wall-crossings of an infinite number of vortex quiver theories are neatly and collectively encoded by 3d determinant of such extra chiral fields.

Built on

M. E. Peskin, Mandelstam-’t hooft duality in abelian lattice models , Annals of Physics 113
1978
Earlier work this paper cites.
C. Dasgupta and B. I. Halperin, Phase transition in a lattice model of superconductivity , Phys. Rev. Lett. 47
1981
Earlier work this paper cites.
E. J. Weinberg, Fundamental Monopoles in Theories With Arbitrary Symmetry Breaking , Nucl. Phys. B203
1982
Earlier work this paper cites.
E. Witten, Constraints on Supersymmetry Breaking , Nucl. Phys. B202
1982
Earlier work this paper cites.
C. Beem, T. Dimofte and S. Pasquetti, Holomorphic Blocks in Three Dimensions , JHEP 12
Original
1986
Earlier work this paper cites.
L. Alvarez-Gaume, SUPERSYMMETRY AND INDEX THEORY , in 1984 NATO ASI on Supersymmetry Bonn, Germany, August 20-31, 1984 , pp. 1–44, 1986
1986
Earlier work this paper cites.
L. C. Jeffrey and F. C. Kirwan, Localization for nonabelian group actions , in eprint arXiv:alg-geom/9307001 , July, 1993
1993
Earlier work this paper cites.
K. A. Intriligator and N. Seiberg, Mirror symmetry in three-dimensional gauge theories , Phys. Lett. B387
1996
Earlier work this paper cites.
O. Aharony, IR duality in d = 3 N=2 supersymmetric USp(2N(c)) and U(N(c)) gauge theories , Phys. Lett. B404
1997
Earlier work this paper cites.
O. Aharony, A. Hanany, K. A. Intriligator, N. Seiberg and M. J. Strassler, Aspects of N=2 supersymmetric gauge theories in three-dimensions , Nucl. Phys. B499
1997
Earlier work this paper cites.
A. Hanany and E. Witten, Type IIB superstrings, BPS monopoles, and three-dimensional gauge dynamics , Nucl. Phys. B492
1997
Earlier work this paper cites.
A. Kapustin and M. J. Strassler, On mirror symmetry in three-dimensional Abelian gauge theories , JHEP 04
1999
Earlier work this paper cites.
M. Brion and M. Vergne, Arrangements of hyperplanes I: Rational functions and Jeffrey-Kirwan residue , ArXiv Mathematics e-prints (Mar., 1999) , [ math/9903178 ]
1999
Earlier work this paper cites.
F. Denef, Quantum quivers and Hall / hole halos , JHEP 10
2002
Earlier work this paper cites.
N. A. Nekrasov, Seiberg-Witten prepotential from instanton counting , Adv. Theor. Math. Phys. 7
2003
Earlier work this paper cites.
A. Hanany and D. Tong, Vortices, instantons and branes , JHEP 07
2003
Earlier work this paper cites.
A. Givental and Y.-P. Lee, Quantum K-theory on flag manifolds, finite-difference Toda lattices and quantum groups , Inventiones Mathematicae. 151
2003
Earlier work this paper cites.
A. Szenes and M. Vergne, Toric reduction and a conjecture of Batyrev and Materov , Inventiones Mathematicae 158
2004
Earlier work this paper cites.
E. J. Weinberg and P. Yi, Magnetic Monopole Dynamics, Supersymmetry, and Duality , Phys. Rept. 438
2007
Earlier work this paper cites.
F. van de Bult, Hyperbolic Hypergeometric Functions , Thesis (2007)
2007
Earlier work this paper cites.
J. Bhattacharya, S. Bhattacharyya, S. Minwalla and S. Raju, Indices for Superconformal Field Theories in 3,5 and 6 Dimensions , JHEP 02
Original
2008
Earlier work this paper cites.
A. Giveon and D. Kutasov, Seiberg Duality in Chern-Simons Theory , Nucl. Phys. B812
Original
2009
Earlier work this paper cites.
D. Gaiotto and E. Witten, S-Duality of Boundary Conditions In N=4 Super Yang-Mills Theory , Adv. Theor. Math. Phys. 13
Original
2009
Earlier work this paper cites.
S. Kim, The Complete superconformal index for N=6 Chern-Simons theory , Nucl. Phys. B821
Original
2009
Earlier work this paper cites.
J. Bhattacharya and S. Minwalla, Superconformal Indices for N = 6 Chern Simons Theories , JHEP 01
Original
2009
Earlier work this paper cites.
A. Kapustin, B. Willett and I. Yaakov, Exact Results for Wilson Loops in Superconformal Chern-Simons Theories with Matter , JHEP 03
Original
2010
Earlier work this paper cites.
C. Krattenthaler, V. P. Spiridonov and G. S. Vartanov, Superconformal indices of three-dimensional theories related by mirror symmetry , JHEP 06
Original
2011
Earlier work this paper cites.
F. Benini, C. Closset and S. Cremonesi, Comments on 3d Seiberg-like dualities , JHEP 10
Original
2011
Earlier work this paper cites.

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