algebraic quantum field theory (perturbative, on curved spacetimes, homotopical)
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interacting field quantization
superalgebra and (synthetic ) supergeometry
The special case of super Yang-Mills theory over a spacetime of dimension 3 and with number of supersymmetries.
Both the Coulomb branches and the Higgs branch of D=3 N=4 super Yang-Mills theory are hyperkähler manifolds. In special cases they are compact hyperkähler manifolds (e.g. dBHOO 96).
The , SYM theory can be obtained by dimensional reduction from N=2 D=4 super Yang-Mills theory (Seiberg-Witten 96)
A version of mirror symmetry acts on the , SYM moduli space of vacua and exchanges the Coulomb branch with the Higgs branch. (Intriligator-Seiberg 96)
See also the discussion at symplectic duality.
A topological twist of D=3 N=4 super Yang-Mills theory is Rozansky-Witten theory.
The construction of D=3 N=4 super Yang-Mills theory by dimensional reduction from N=2 D=4 super Yang-Mills theory was first considered in
Discussion as the worldvolume-theory of D3-D5 brane intersections:
Review of the moduli space of vacua:
Via KK-compactification from little string theory:
and from heterotic string theory on ADE-singularities:
See also:
On mirror symmetry for D=3 N=4 super Yang-Mills theory
The mirror symmetry operation was discussed in
Discussion with emphasis of Higgs branches/Coulomb branches as Hilbert schemes of points
Jan de Boer, Kentaro Hori, Hirosi Ooguri, Yaron Oz, Mirror Symmetry in Three-Dimensional Gauge Theories, Quivers and D-branes, Nucl. Phys. B493:101-147, 1997 (arXiv:hep-th/9611063)
Jan de Boer, Kentaro Hori, Hirosi Ooguri, Yaron Oz, Zheng Yin, Mirror Symmetry in Three-Dimensional Gauge Theories, and D-Brane Moduli Spaces, Nucl. Phys. B493:148-176, 1997 (arXiv:hep-th/9612131)
Mathew Bullimore, Andrea Ferrari, Heeyeon Kim, Supersymmetric Ground States of 3d Gauge Theories on a Riemann Surface (arXiv:2105.08783)
Lift to M-theory:
Review of Coulomb branches of D=3 N=4 super Yang-Mills theory:
Identification of the Coulomb branch of D=3 N=4 super Yang-Mills theory with the moduli space of monopoles in Yang-Mills theory:
N. Dorey, V. V. Khoze, M. P. Mattis, David Tong, S. Vandoren, Instantons, Three-Dimensional Gauge Theory, and the Atiyah-Hitchin Manifold, Nucl. Phys. B502 (1997) 59-93 (arXiv:hep-th/9703228)
David Tong, Three-Dimensional Gauge Theories and ADE Monopoles, Phys. Lett. B448 (1999) 33-36 (arXiv:hep-th/9803148)
Mathew Bullimore, Tudor Dimofte, Davide Gaiotto, The Coulomb Branch of 3d Theories, Commun. Math. Phys. (2017) 354: 671 (arXiv:1503.04817)
On D=3 N=4 super Yang-Mills theories with compact hyperkähler manifold Coulomb branches obtained by KK-compactification of little string theories:
The Rozansky-Witten invariants of these moduli spaces:
On a mathematical definition of quantum Coulomb branches of D=3 N=4 super Yang-Mills theory:
Hiraku Nakajima, Introduction to a provisional mathematical definition of Coulomb branches of 3-dimensional gauge theories (arXiv:1706.05154)
Hiraku Nakajima, Towards a mathematical definition of Coulomb branches of 3-dimensional gauge theories, I (arXiv:1503.03676)
Alexander Braverman, Michael Finkelberg, Hiraku Nakajima, Towards a mathematical definition of Coulomb branches of 3-dimensional gauge theories, II, Adv. Theor. Math. Phys. 22 (2018) 1071-1147 (arXiv:1601.03586)
Alexander Braverman, Michael Finkelberg, Hiraku Nakajima, Line bundles over Coulomb branches (arXiv:1805.11826)
(relation to Hilbert schemes)
Identification of Higgs branches/Coulomb branches in D=3 N=4 super Yang-Mills theory with Hilbert schemes of points of complex curves:
Jan de Boer, Kentaro Hori, Hirosi Ooguri, Yaron Oz, Mirror Symmetry in Three-Dimensional Gauge Theories, Quivers and D-branes, Nucl. Phys. B493:101-147, 1997 (arXiv:hep-th/9611063)
Jan de Boer, Kentaro Hori, Hirosi Ooguri, Yaron Oz, Zheng Yin, Mirror Symmetry in Three-Dimensional Gauge Theories, and D-Brane Moduli Spaces, Nucl. Phys. B493:148-176, 1997 (arXiv:hep-th/9612131)
Stefano Cremonesi, Amihay Hanany, Alberto Zaffaroni, around (4.4) of: Monopole operators and Hilbert series of Coulomb branches of 3d gauge theories, JHEP 01 (2014) 005 (arXiv:1309.2657)
Alexander Braverman, Michael Finkelberg, Hiraku Nakajima, Line bundles over Coulomb branches (arXiv:1805.11826)
Mykola Dedushenko, Yale Fan, Silviu Pufu, Ran Yacoby, Section E.2 of: Coulomb Branch Quantization and Abelianized Monopole Bubbling, JHEP 10 (2019) 179 (arXiv:1812.08788)
Discussion of the Witten index of D=3 N=4 super Yang-Mills theory:
Mathew Bullimore, Andrea E.V. Ferrari, Heeyeon Kim, Twisted Indices of 3d N=4 Gauge Theories and Enumerative Geometry of Quasi-Maps (arXiv:1812.05567)
Davide Gaiotto, Tadashi Okazaki, Sphere correlation functions and Verma modules (arXiv:1911.11126)
Mathew Bullimore, Samuel Crew, Daniel Zhang, Boundaries, Vermas, and Factorisation (arXiv:2010.09741)
using discussion in
See also on the Witten index for D=3 N=2 super Yang-Mills theory:
On Wilson loop operators in D=3 N=4 super Yang-Mills theory:
Last revised on January 24, 2024 at 04:44:39. See the history of this page for a list of all contributions to it.