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Surface Operators in N=2 4d Gauge Theories · Around

2009

Surface Operators in N=2 4d Gauge Theories

Gaiotto, Davide

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N=2 four dimensional gauge theories admit interesting half BPS surface operators preserving a (2,2) two dimensional SUSY algebra.

Typical examples are (2,2) 2d sigma models with a flavor symmetry which is coupled to the 4d gauge fields.
Interesting features of such 2d sigma models, such as (twisted) chiral rings, and the tt* geometry, can be carried over to the surface operators, and are affected in surprising ways by the coupling to 4d degrees of freedom.
We will describe in detail a relation between the parameter space of twisted couplings of the surface operator and the Seiberg-Witten geometry of the bulk theory.

Built on

M. F. Atiyah, “Instantons in Two and Four Dimensions,” Comm. Math. Phys
1984
Earlier work this paper cites.
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1991
Earlier work this paper cites.
S. Cecotti and C. Vafa, “On classification of N=2 supersymmetric theories,” Commun. Math. Phys. 158
1993
Earlier work this paper cites.

Similar

E. Witten, “Solutions of four-dimensional field theories via M- theory,” Nucl. Phys. B500
1997
Cited alongside, same era.
S. Katz, P. Mayr, and C. Vafa, “Mirror symmetry and exact solution of 4D N = 2 gauge theories. I,” Adv. Theor. Math. Phys
1998
Cited alongside, same era.
A. Kapustin, “D(n) quivers from branes,” JHEP
1998
Cited alongside, same era.
D. Gaiotto, “N=2 dualities,” arXiv:0904.2715 [hep-th]
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Cited in the paper.
D. Gaiotto, G. W. Moore, and A. Neitzke, “Wall-crossing, Hitchin Systems, and the WKB Approximation,” arXiv:0907.3987 [hep-th]
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L. F. Alday, D. Gaiotto, and Y. Tachikawa, “Liouville Correlation Functions from Four-Dimensional Gauge Theories,” arXiv:0906.3219 [hep-th]
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Cited in the paper.
N. Drukker, D. R. Morrison, and T. Okuda, “Loop Operators and S-Duality from Curves on Riemann Surfaces,” arXiv:0907.2593 [hep-th]
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Cited in the paper.
N. Drukker, J. Gomis, T. Okuda, and J. Teschner, “Gauge Theory Loop Operators and Liouville Theory,” arXiv:0909.1105 [hep-th]
Original
Cited in the paper.
L. F. Alday, D. Gaiotto, S. Gukov, Y. Tachikawa, and H. Verlinde, “Loop and surface operators in N=2 gauge theory and Liouville modular geometry,” arXiv:0909.0945 [hep-th]
Original
Cited in the paper.
S. Gukov and E. Witten, “Gauge theory, ramification, and the geometric langlands program,” arXiv:hep-th/0612073
Cited in the paper.
D. Tong, “Quantum Vortex Strings: a Review,” arXiv:0809.5060 [hep-th]
Original
Cited in the paper.
S. Cecotti
Cited in the paper.

Then

A. Hanany and K. Hori, “Branes and 𝒩 = 2 {\mathcal{N}}\!=2 Theories in Two Dimensions,” Nucl. Phys. B513
Original
1998
Later among the works it cites.
H. Ooguri and C. Vafa, “Knot invariants and topological strings,” Nucl. Phys. B577
2000
Later among the works it cites.

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