Vortices, instantons and branes

By A. Hanany, David Tong. 2003

466 citations recorded by the source corpus.

The purpose of this paper is to describe a relationship between the moduli space of vortices and the moduli space of instantons. We study charge vortices in Yang-Mills-Higgs theories and show that the moduli space is isomorphic to a special lagrangian submanifold of the moduli space of instantons in non-commutative Yang-Mills theories. This submanifold is the fixed point set of a action on the instanton moduli space which rotates the instantons in a plane. To derive this relationship, we present a D-brane construction in which the dynamics of vortices is described by the Higgs branch of a gauge theory with 4 supercharges which is a truncation of the familiar ADHM gauge theory. We further describe a moduli space construction for semi-local vortices, lumps in the and grassmannian sigma-models, and vortices on the non-commutative plane. We argue that this relationship between vortices and instantons underlies many of the quantitative similarities between quantum field theories in two and four dimensions.

Subfields: Mathematical Physics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/63d0f3a70acd9d4bcdd566cef0705b5b6547be9b

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Citations in the corpus

Vortex strings and four-dimensional gauge dynamics (2004, background): “…curve has a special property: it degenerates [18] F (t, u) = ( t− Nc ∏ i=1 (u−mi) ) ( u− ΛNc ) (7) This form of the curve occurs naturally in the M-theory construction of [19], where the degeneration corresponds to the fact that one of the IIA NS5 branes remains unbent upon its ascent to M-theory.”
TOPICAL REVIEW: Solitons in the Higgs phase: the moduli matrix approach (2006, methodology): “Then we find a complete relationship between our moduli space and the moduli space constructed by the Kähler quotient, which was given in [76] by using a D-brane configuration in string theory.”
Partition Functions of $${\mathcal{N}=(2,2)}$$N=(2,2) Gauge Theories on S2 and Vortices (2012, methodology): “This asymmetry is inherent to the brane inspired construction of vortex moduli spaces of [37], where the k-vortex theory for a 2d U (N ) gauge theory with N f fundamentals is a 0d U (k) gauge theory with one adjoint, N fundamentals and N f − N antifundamentals.”
Quantum vortex strings: A review (2008, unknown): “There are tantalizing hints that N = (0, 2) worldsheet theories may transform in an interesting fashion under the ubiquitous Nf → Nf − Nc transformation [10, 104] and various comments on the relationship to Seiberg duality have been made in [105, 106].”
The effective theory of long strings (2013, background): “Some of the well-known examples come from supersymmetric QCD-like theories, see [5,6,7], the reviews [8,9,10], and references therein.”
Exact results in D = 2 supersymmetric gauge theories (2012, unknown): “pace Mfp ig;k vortex of congurations with kvortices admits an ADHM-like construction, which can be understood as the supersymmetric vacua of a certain gauged matrix model preserving two supercharges [27,31,32]. The relevant representations of the supersymmetry algebra can be obtained from the dimens”
2d index and surface operators (2013, methodology): “pe in N= 2 theories of class S was computed in [13] via indirect means. For a discussion on nonabelian semi-local vortex strings, see e.g. [33]. Corresponding brane construction has been described in [34]. In this paper, we utilize the construction of the surface operator as the 4dgauge theory coupl”