Branes and supergroups
type: Item
instance of: scholarly article
title: Branes and supergroups
zbMATH Open document ID: 1326.81210
author: Victor Mikhaylov
author: Edward Witten
published in: Communications in Mathematical Physics
publication date: 2015-10-07T00:00:00Z
full work available at URL: https://arxiv.org/abs/1410.1175
review text: This bulky article evolved out of previous work by the second author [Quantum Topol. 3, No. 1, 1--137 (2012; Zbl 1241.57041)]. Adopting an elegant geometric approach, this advanced text describes methods for understanding the three-dimensional supergroup Chern-Simon theory and how dualities act on line and surface operators. Many mathematical details are supplied which make the paper reasonably self-contained. The authors consider what they call \textit{a two-sided problem}: a 5-brane of NS type with \(m\) D3-branes ending on it from the left and \(n\) D3-branes from the right. And so the paper is devoted primarily to the study of D3-branes interacting on both sides of a single fivebrane. Contrary to the \textit{one-sided} case, a supergroup \(\mathrm{U}(m|n)\) is associated to the Chern-Simons theory. A dual magnetic description is obtained by \(S\)-duality. The paper is organized as follows. Section 1 provides an introduction, Section 2 describes in detail the relation of the two-sided system to supergroups. In Section 3, line and surface operators are analyzed. Section 4 describes the \(S\)-duality. In Section 5, an O3 plane is incorporated and orthosymplectic groups and the novel duality are discussed. A symmetry-breaking process is analyzed in Section 6, while in Section 7 the magnetic description is lifted to a D4-D6 system and an analogue of Khovanov homology for supergroups is described. Many details are provided in five appendices. This paper is an outstanding resource for graduate students and researchers in mathematical physics.
reviewed by: Gert Roepstorff
Mathematics Subject Classification ID: 81T60
Mathematics Subject Classification ID: 81T30
Mathematics Subject Classification ID: 81T10
Mathematics Subject Classification ID: 81R40
zbMATH DE Number: 6490963
zbMATH Keywords: super Chern-Simon theory
zbMATH Keywords: branes
zbMATH Keywords: duality
zbMATH Keywords: supergroups
zbMATH Keywords: magnetic description
zbMATH Keywords: orthosymplectic groups
zbMATH Keywords: symmetry breaking
MaRDI profile type: Publication
OpenAlex ID: W2105233747
arXiv ID: 1410.1175
cites work: Fivebranes and knots
cites work: Supersymmetric boundary conditions in \(\mathcal{N}=4\) super Yang-Mills theory
cites work: Electric-magnetic duality and the geometric Langlands program
cites work: Q3108683
cites work: Q3108747
cites work: A categorification of the Jones polynomial
cites work: Khovanov-Rozansky homology and topological strings
cites work: Knot invariants and topological strings.
cites work: Janus configurations, Chern-Simons couplings, and the {\(\theta\)}-angle in \(\mathcal{N} = 4\) super Yang-Mills theory
cites work: Chern-Simons-Rozansky-Witten topological field theory
cites work: Baryons and branes in anti-de Sitter space
cites work: On orientifolds, discrete torsion, branes and M-theory
cites work: Mirror symmetry by O3-planes
cites work: Orientifolds, branes, and duality of 4D gauge theories
cites work: \(S\)-duality of boundary conditions in \({\mathcal N}=4\) super Yang-Mills theory
cites work: Odd Khovanov homology
cites work: An odd categorification of \(U_q(\mathfrak{sl}_2)\)
cites work: Braid group representations arising from quantum supergroups with arbitrary q and link polynomials
cites work: QUANTUM SUPERGROUPS, LINK POLYNOMIALS AND REPRESENTATION OF THE BRAID GENERATOR
cites work: Three-manifold invariants arising from \(U_q(\text{osp}(1|2))\)
cites work: Quantum superalgebras at roots of unity and topological invariants of three-manifolds
cites work: Type IIB superstrings, BPS monopoles, and three-dimensional gauge dynamics
cites work: Quantum field theory and the Jones polynomial
cites work: Q4168737
cites work: Superspace conformal field theory
cites work: Q4515164
cites work: Q4869244
cites work: On the Superdimension of an Irreducible Representation of a Basic Classical Lie Superalgebra
cites work: Q3892399
cites work: Laplace operators of infinite-dimensional Lie algebras and theta functions
cites work: Cohomology of generalized supergrassmannians and character formulae for basic classical Lie superalgebras
cites work: Localization for Wilson loops in Chern-Simons theory
cites work: On the solutions of generalized Bogomolny equations
cites work: \(\underline{SW}\)=Milnor torsion
cites work: Q3597344
cites work: Rigid surface operators
cites work: On framings of 3-manifolds
cites work: Q4816888
cites work: INTRODUCTION TO COHOMOLOGICAL FIELD THEORIES
cites work: Reidemeister torsion, the Alexander polynomial and \(U(1,1)\) Chern-Simons theory
cites work: Q4912934
cites work: Spectral asymmetry and Riemannian Geometry. I
cites work: Spectral asymmetry and Riemannian geometry. II
cites work: Spectral asymmetry and Riemannian geometry. III
cites work: The Nahm Pole Boundary Condition
cites work: DUALITY IN osp(1|2) CONFORMAL FIELD THEORY AND LINK INVARIANTS
cites work: ON THE Uq(osp(1|2n)) AND U-q(so(2n + 1)) UNCOLORED QUANTUM LINK INVARIANTS
cites work: Finite-dimensional representations of \(U_ q(osp (1/2n))\) and its connection with quantum \(so(2n+1)\)
cites work: A remarkable connection between the representations of the Lie superalgebras osp(1,2n) and the Lie algebras o(2n+1)
cites work: A strong coupling test of \(S\)-duality
cites work: Dimension and character formulas for Lie supergroups
cites work: Representations of orthosymplectic superalgebras. II. Young diagrams and weight space techniques
cites work: Young diagrams, supercharacters of OSp(M/N) and modification rules
cites work: Supersymmetric index in four-dimensional gauge theories

Branes and supergroups (cites work)
cites work: Knot invariants from four-dimensional gauge theory

Branes and supergroups (cites work)
cites work: Cohomological reduction of sigma models

Branes and supergroups (cites work)
cites work: Khovanov Homology And Gauge Theory

Branes and supergroups (cites work)
cites work: Two Lectures On The Jones Polynomial And Khovanov Homology

Branes and supergroups (cites work)
cites work: Supersymmetry and Morse theory

Branes and supergroups (cites work)
cites work: Q4434432

Branes and supergroups (cites work)
cites work: Quadruply-graded colored homology of knots

Branes and supergroups (cites work)
cites work: Topological quantum field theory

Branes and supergroups (cites work)
cites work: Cohomology and support varieties for Lie superalgebras

Branes and supergroups (cites work)
cites work: Perturbative expansion of Chern-Simons theory with non-compact Gauge group

Branes and supergroups (cites work)
cites work: On holomorphic factorization of WZW and coset models

Branes and supergroups (cites work)
cites work: Computer calculation of Witten's 3-manifold invariant

Branes and supergroups (DOI)
DOI: 10.1007/S00220-015-2449-Y

Branes and supergroups (Recommended article)
Recommended article: Supergravities on branes
Similarity Score: 0.92484725
Recommender Run: Recommender Run 3

Branes and supergroups (Recommended article)
Recommended article: Geometry of branes on supergroups
Similarity Score: 0.922565
Recommender Run: Recommender Run 3

Branes and supergroups (Recommended article)
Recommended article: Branes and fundamental groups
Similarity Score: 0.9157252
Recommender Run: Recommender Run 3

Branes and supergroups (Recommended article)
Recommended article: Super D-branes
Similarity Score: 0.91408145
Recommender Run: Recommender Run 3

Branes and supergroups (Recommended article)
Recommended article: Q3365257
Similarity Score: 0.9140814
Recommender Run: Recommender Run 3

Branes and supergroups (Recommended article)
Recommended article: Q4267866
Similarity Score: 0.9140814
Recommender Run: Recommender Run 3

Branes and supergroups (Recommended article)
Recommended article: Branes, fermions, and superspace dualities
Similarity Score: 0.9086164
Recommender Run: Recommender Run 3

Branes and supergroups (Recommended article)
Recommended article: Supersymmetry and the brane-world
Similarity Score: 0.90815663
Recommender Run: Recommender Run 3

Branes and supergroups (Recommended article)
Recommended article: Q4507526
Similarity Score: 0.9039844
Recommender Run: Recommender Run 3

Branes and supergroups (Recommended article)
Recommended article: Supersymmetry and the brane-world
Similarity Score: 0.9036427
Recommender Run: Recommender Run 3