non-Abelian Tensor Multiplet Research Articles

Covariant quantisation of tensor multiplet models

The Batalin-Vilkovisky formalism is applied to quantise the N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 1 supersymmetric generalisation of the Freedman-Townsend (FT) model, which was proposed by Lindström and Roček in 1983 in Minkowski superspace and is lifted to a supergravity background in this paper. This super FT theory describes a non-Abelian tensor multiplet and is known to be classically equivalent to a supersymmetric nonlinear sigma model. Using path integral considerations, we demonstrate that this equivalence holds at the quantum level in the sense that the quantum supercurrents in the two theories coincide. A modified Faddeev-Popov procedure is employed to quantise models for the N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 2 tensor multiplet in harmonic superspace. The obtained results agree with those derived by applying the Batalin-Vilkovisky scheme within the harmonic superspace setting.

Odd-dimensional self-duality for non-Abelian tensor-multiplet in D = 3 + 2 as master theory of integrable-systems

We present N=2 supersymmetric non-Abelian duality-symmetry between a tensor multiplet and an extra vector multiplet in D=3+2 dimensions. Our system has the Yang-Mills (YM) vector multiplet (AμI,λI), a tensor-multiplet (BμνI,χI,φI), and an extra vector multiplet (CμI,ρI,σI). The index I=1,2,⋯,dimG is for the adjoint representation of a non-Abelian group G. The AμI is the conventional YM gauge field, BμνI is a non-Abelian tensor field, while φI and σI are scalar fields. The λI,χI and ρI are Majorana fermions in the 2 of Sp(1). The BμνI and CμI-fields have their respective field-strengths defined by GμνρI≡+3D⌊⌈μBνρ⌋⌉I+3fIJKF⌊⌈μνJCρ⌋⌉K and HμνI≡+2D⌊⌈μCν⌋⌉I+mBμνI+fIJKϕJHμνK−fIJKσJFμνK. The duality relationship is HμνI=(1/6)ϵμνρστGρστI−(1/2)fIJK(λ‾JγμνχK), with its super-partner relationships: φI=−σI,χI=−ρI. Since HστI contains mBστI linearly, this is a ‘massive’ self-dual relationship. Interestingly, the closure of supersymmetries shows the intrinsic global scale symmetry: δζ(BμνI,χI,φI,CμI,ρI,σI)=+mζ(BμνI,χI,φI,CμI,ρI,σI). By certain dimensional-reduction scheme into D=2+2, we show that self-dual supersymmetric tensor multiplet is generated. We deduce that our present theory in D=3+2 can serve as the underlying ‘Master Theory’ of a similar system in D=2+2.

Towards an M5-brane model I: A 6d superconformal field theory

We present an action for a six-dimensional superconformal field theory containing a non-abelian tensor multiplet. All of the ingredients of this action have been available in the literature. We bring these pieces together by choosing the string Lie 2-algebra as a gauge structure, which we motivated in previous work. The kinematical data contains a connection on a categorified principal bundle, which is the appropriate mathematical description of the parallel transport of self-dual strings. Our action can be written down for each of the simply laced Dynkin diagrams, and each case reduces to a four-dimensional supersymmetric Yang–Mills theory with corresponding gauge Lie algebra. Our action also reduces nicely to an M2-brane model which is a deformation of the Aharony-Bergman-Jafferis-Maldacena (ABJM) model. While this action is certainly not the desired M5-brane model, we regard it as a key stepping stone towards a potential construction of the (2, 0)-theory.

N = (2,0) self-dual non-Abelian tensor multiplet in D = 3 + 3 generates N = (1,1) self-dual systems in D = 2 + 2

We formulate an N=(2,0) system in D=3+3 dimensions consisting of a Yang–Mills (YM)-multiplet (AˆμˆI,λˆI), a self-dual non-Abelian tensor multiplet (BˆμˆνˆI,χˆI,φˆI), and an extra vector multiplet (CˆμˆI,ρˆI). We next perform the dimensional reductions of this system into D=2+2, and obtain N=(1,1) systems with a self-dual YM-multiplet (AμI,λI), a self-dual tensor multiplet (BμνI,χI,φI), and an extra vector multiplet (CμI,ρI). In D=2+2, we reach two distinct theories: ‘Theory-I’ and ‘Theory-II’. The former has the self-dual field-strength Hμν(+)I of CμI already presented in our recent paper, while the latter has anti-self-dual field strength Hμν(−)I. As an application, we show that Theory-II actually generates supersymmetric-KdV equations in D=1+1. Our result leads to a new conclusion that the D=3+3 theory with non-Abelian tensor multiplet can be a ‘Grand Master Theory’ for self-dual multiplet and self-dual YM-multiplet in D=2+2, that in turn has been conjectured to be the ‘Master Theory’ for all supersymmetric integrable theories in D≤3.

Six-Dimensional Superconformal Field Theories from Principal 3-Bundles over Twistor Space

We construct manifestly superconformal field theories in six dimensions which contain a non-Abelian tensor multiplet. In particular, we show how principal 3-bundles over a suitable twistor space encode solutions to these self-dual tensor field theories via a Penrose-Ward transform. The resulting higher or categorified gauge theories significantly generalise those obtained previously from principal 2-bundles in that the so-called Peiffer identity is relaxed in a systematic fashion. This transform also exposes various unexplored structures of higher gauge theories modelled on principal 3-bundles such as the relevant gauge transformations. This enables us to formulate the non-Abelian differential cohomology that describes principal 3-bundles with connective structures.

Non-Abelian Tensor Multiplet Equations from Twistor Space

We establish a Penrose–Ward transform yielding a bijection between holomorphic principal 2-bundles over a twistor space and non-Abelian self-dual tensor fields on six-dimensional flat space-time. Extending the twistor space to supertwistor space, we derive sets of manifestly \({\mathcal{N} = (1, 0)}\) and \({\mathcal{N} = (2, 0)}\) supersymmetric non-Abelian constraint equations containing the tensor multiplet. We also demonstrate how this construction leads to constraint equations for non-Abelian supersymmetric self-dual strings.

A nonabelian (1, 0) tensor multiplet theory in 6D

We construct a general nonabelian (1,0) tensor multiplet theory in six dimensions. The gauge field of this (1,0) theory is non-dynamical, and the theory contains a continuous parameter $b$. When $b=1/2$, the (1,0) theory possesses an extra discrete symmetry enhancing the supersymmetry to (2,0), and the theory turns out to be identical to the (2,0) theory of Lambert and Papageorgakis (LP). Upon dimension reduction, we obtain a general ${\cal N}=1$ supersymmetric Yang-Mills theory in five dimensions. The applications of the theories to D4 and M5-branes are briefly discussed.

Self-dual non-Abelian [formula omitted] tensor multiplet in [formula omitted] dimensions

We present a self-dual non-Abelian N=1 supersymmetric tensor multiplet in D=2+2 space–time dimensions. Our system has three on-shell multiplets: (i) The usual non-Abelian Yang–Mills multiplet (AμI,λI), (ii) a non-Abelian tensor multiplet (BμνI,χI,φI), and (iii) an extra compensator vector multiplet (CμI,ρI). Here the index I is for the adjoint representation of a non-Abelian gauge group. The duality symmetry relations are GμνρI=−ϵμνρσ∇σφI, FμνI=+(1/2)ϵμνρσFρσI, and HμνI=+(1/2)ϵμνρσHρσI, where G and H are respectively the field strengths of B and C. The usual problem with the coupling of the non-Abelian tensor is avoided by non-trivial Chern–Simons terms in the field strengths GμνρI and HμνI. For an independent confirmation, we re-formulate the component results in superspace. As applications of embedding integrable systems, we show how the N=2, r=3 and N=3, r=4 flows of generalized Korteweg–de Vries equations are embedded into our system.

N=1non-Abelian tensor multiplet in four dimensions

We carry out the $N=1$ supersymmetrization of a physical non-Abelian tensor with nontrivial consistent couplings in four dimensions. Our system has three multiplets: (i) The usual non-Abelian vector multiplet $(A_{\ensuremath{\mu}}{}^{I},{\ensuremath{\lambda}}^{I})$, (ii) A non-Abelian tensor multiplet (TM) $(B_{\ensuremath{\mu}\ensuremath{\nu}}{}^{I},{\ensuremath{\chi}}^{I},{\ensuremath{\varphi}}^{I})$, and (iii) A compensator vector multiplet (CVM) $(C_{\ensuremath{\mu}}{}^{I},{\ensuremath{\rho}}^{I})$. All of these multiplets are in the adjoint representation of a non-Abelian group $G$. Unlike topological theory, all of our fields are propagating with kinetic terms. The $C_{\ensuremath{\mu}}{}^{I}$-field plays the role of a Stueckelberg compensator absorbed into the longitudinal component of $B_{\ensuremath{\mu}\ensuremath{\nu}}{}^{I}$. We give not only the component Lagrangian, but also a corresponding superspace reformulation, reconfirming the total consistency of the system. The adjoint representation of the TM and CVM is further generalized to an arbitrary real representation of general $SO(N)$ gauge group. We also couple the globally $N=1$ supersymmetric system to supergravity, as an additional nontrivial confirmation.

Branes from a non-Abelian (2,0) tensor multiplet with 3-algebra

In this paper, we study the equations of motion for non-Abelian tensor multiplets in six dimensions, which were recently proposed by Lambert and Papageorgakis. Some equations are regarded as constraint equations. We employ a loop extension of the Lorentzian three-algebra (3-algebra) and examine the equations of motion around various solutions of the constraint equations. The resultant equations take forms that allow Lagrangian descriptions. We find various (5 + d)-dimensional Lagrangians and investigate the relation between them from the viewpoint of M-theory duality.

Five-dimensional super Yang-Mills theory from ABJM theory

We derive five-dimensional super Yang-Mills theory from mass-deformed ABJM theory by expanding about S 2 for large Chern-Simons level K. We obtain the Yang-Mills coupling constant \( g_{Y\;M}^2 = {{{4{\pi^2}R}} \left/ {K} \right.} \). If we consider \( {{{{S^3}}} \left/ {{{\mathbb{Z}_K}}} \right.} \) as a fiber bundle over S 2 then R/K is the circumference of the fiber. The value on the coupling constant agrees with what one gets by compactifying M five-brane on that fiber. For this computation we take R, K → ∞ while keeping R/K at a fixed finite value. We also study mass deformed star-three-product BLG theory at K = 1 and R → ∞. In that limit we obtain Lorentz covariant supersymmetry variations and gauge variations of a non-Abelian tensor multiplet.

The non-abelian tensor multiplet in loop space

We introduce a non-Abelian tensor multiplet directly in the loop space associated with flat six-dimensional Minkowski space-time, and derive the supersymmetry variations for on-shell ${\cal{N}}=(2,0)$ supersymmetry.