Classical self-dual strings in d=6, (2,0) theory from afar

We show how one can get solitonic strings in a six-dimensional (2,0) supersymmetric theory by incorporating a nonlinear interaction term. We derive a zero force condition between parallel strings, and compute a metric on a moduli space which is $R^4$ when the strings are far apart. When compactifying the strings on a two-torus we show that, in the limit of vanishing two-torus, one regains the moduli space of two widely separated dyons of equal magnetic charges in four dimensions.Comment: 13 pages, clarifications and added reference

A reparametrization invariant surface ordering

We introduce a notion of a non-Abelian loop gauge field defined on points in loop space. For this purpose we first find an infinite-dimensional tensor product representation of the Lie algebra which is particularly suited for fields on loop space. We define the non-Abelian Wilson surface as a `time' ordered exponential in terms of this loop gauge field and show that it is reparametrization invariant.Comment: 11 pages, clarifications and added ref

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

In this paper, we study the equations of motion for non-Abelian N=(2,0) 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.Comment: 44+1 pages, reference added, typos corrected, and several discussions added; v3, reference added, many typos corrected, the language improved; v4, some typos and references corrected, final version to appear in J. Phys.

Supersymmetric coupling of a self-dual string to a (2,0) tensor multiplet background

We construct an interaction between a (2,0) tensor multiplet in six dimensions and a self-dual string. The interaction is a sum of a Nambu-Goto term, with the tension of the string given by the modulus of the scalar fields of the tensor multiplet, and a non-local Wess-Zumino term, that encodes the electromagnetic coupling of the string to the two-form gauge field of the tensor multiplet. The interaction is invariant under global (2,0) supersymmetry, modulo the equations of motion of a free tensor multiplet. It is also invariant under a local fermionic kappa-symmetry, as required by the BPS-property of the string.Comment: 12 pages, LaTe

Free tensor multiplets and strings in spontaneously broken six-dimensional (2,0) theory

We first review the representations of the six-dimensional (2,0) superalgebra on a free tensor multiplet and on a free string. We then construct a supersymmetric Lagrangian describing a free tensor multiplet. (It also includes a decoupled anti self-dual part of the three-form field strength.) This field theory is then rewritten in variables appropriate for analyzing a situation where the R-symmetry is spontaneously broken by the vacuum expectation values of the scalar moduli fields. Finally, we construct a supersymmetric and kappa-symmetric action for a free string.Comment: 15 pages, LaTe

KK6 from M2 in BLG

We study the possibility that the Kaluza-Klein monopole (KK6) world-volume action may be obtained from the multiple membranes (M2) action which is described by BLG theory. We first point out that the infinite dimensional Lie 3-algebra based on the Nambu-Poisson structure could not only provide three dimensional manifolds to allow M5 from M2, which was studied by previous authors, but also provide five dimensional manifolds to allow KK6 from M2. We next present a possible way that the U(1) field on KK6 world-volume action could be produced form the gauge potential in BLG theory.Comment: Latex, 15 pages. V3: Add theorem 2 to complete proof. V4: Detail physical interpretations and calculations in section

A Non-Abelian Self-Dual Gauge Theory in 5+1 Dimensions

We construct a non-Abelian gauge theory of chiral 2-forms (self-dual gauge fields) in 6 dimensions with a spatial direction compactified on a circle of radius R. It has the following two properties. (1) It reduces to the Yang-Mills theory in 5 dimensions for small R. (2) It is equivalent to the Lorentz-invariant theory of Abelian chiral 2-forms when the gauge group is Abelian. Previous no-go theorems prohibiting non-Abelian deformations of the chiral 2-form gauge theory are circumvented by introducing nonlocality along the compactified dimension.Comment: 23 pages, reference adde

Super-Yang-Mills and M5-branes

We uplift 5-dimensional super-Yang-Mills theory to a 6-dimensional gauge theory with the help of a space-like constant vector $\eta^M$, whose norm determines the Yang-Mills coupling constant. After the localization of $\eta^M$ the 6D gauge theory acquires Lorentzian invariance as well as scale invariance. We discuss KK states, instantons and the flux quantization. The 6D theory admits extended solutions like 1/2 BPS `strings' and monopoles.Comment: 15 pages; minor changes, to appear in JHE

N=8 superconformal gauge theories and M2 branes

Based on recent developments, in this letter we find 2+1 dimensional gauge theories with scale invariance and N=8 supersymmetry. The gauge theories are defined by a Lagrangian and are based on an infinite set of 3-algebras, constructed as an extension of ordinary Lie algebras. Recent no-go theorems on the existence of 3-algebras are circumvented by relaxing the assumption that the invariant metric is positive definite. The gauge group is non compact, and its maximally compact subgroup can be chosen to be any ordinary Lie group, under which the matter fields are adjoints or singlets. The theories are parity invariant and do not admit any tunable coupling constant. In the case of SU(N) the moduli space of vacua contains a branch of the form (R^8)^N/S_N. These properties are expected for the field theory living on a stack of M2 branes.Comment: 14 pages, no figure

BPS States on M5-brane in Large C-field Background

We extensively study BPS solutions of the low energy effective theory of M5-brane in large C-field background. This provides us an opportunity to explore the interactions turned on by C-field background through the Nambu-Poisson structure. The BPS states considered in this paper include the M-waves, the self-dual string (M2 ending on M5), tilted M5-brane, holomorphic embedding of M5-brane and the intersection of two M5-branes along a 3-brane.Comment: 25 pages, reference adde