Self-dual String Research Articles

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.

Non-abelian self-dual strings in six dimensions from four dimensional 1/2-BPS monopoles

We explain a new construction of self-dual string solutions to the non-abelian two-form self-duality equation proposed in [1]. This class of self-dual strings is determined by the BPS monopoles in four-dimensions and the self-dual string charge is given by the charge of the monopole. Our construction covers the SO(4) invariant self-dual string solutions found previously. We have also constructed, based on the 't Hooft–Polyakov monopole, a singular solution that describes two finitely separated M5-branes meeting midway in between. We comment that as BPS monopoles are generally given by the Nahm construction, our construction suggests that a generalized Nahm transform may exist for the non-abelian self-dual strings.

Brane solitons of (1, 0) superconformal theories in six dimensions with hyper-multiplets

We solve the Killing spinor equations of six-dimensional (1, 0) superconformal theories which include hyper-multiplets in all cases. We show that the solutions preserve 1, 2, 3, 4 and 8 supersymmetries. We find models with self-dual string solitons which are smooth and supported by instantons with an arbitrary gauge group, and 3-brane solitons as expected from the M-brane intersection rules.

Non-abelian self-dual string and M2-M5 branes intersection in supergravity

We consider the non-abelian theory (http://arxiv.org/abs/arXiv:1203.4224) for an arbitrary number $N_5$ of five-branes and construct self-dual string solution with an arbitrary $N_2$ unit of self-dual charges. This generalizes the previous solution of non-abelian self-dual string (http://arxiv.org/abs/arXiv:1207.1095) of $N_5=2, N_2=1$. The radius-transverse distance relation describing the M2-branes spike, particularly its dependence on $N_2$ and $N_5$, is obtained and is found to agree precisely with the supergravity description of an intersecting M2-M5 branes system.

On twistors and conformal field theories from six dimensions

We discuss chiral zero-rest-mass field equations on six-dimensional space-time from a twistorial point of view. Specifically, we present a detailed cohomological analysis, develop both Penrose and Penrose–Ward transforms, and analyse the corresponding contour integral formulæ. We also give twistor space action principles. We then dimensionally reduce the twistor space of six-dimensional space-time to obtain twistor formulations of various theories in lower dimensions. Besides well-known twistor spaces, we also find a novel twistor space amongst these reductions, which turns out to be suitable for a twistorial description of self-dual strings. For these reduced twistor spaces, we explain the Penrose and Penrose–Ward transforms as well as contour integral formulæ.

Magnetic domains

Recently a Nahm transform has been discovered for magnetic bags, which are conjectured to arise in the large n limit of magnetic monopoles with charge n. We interpret these ideas using string theory and present some partial proofs of this conjecture. We then extend the notion of bags and their Nahm transform to higher gauge theories and arbitrary domains. Bags in four dimensions conjecturally describe the large n limit of n self-dual strings. We show that the corresponding Basu-Harvey equation is the large n limit of an equation describing n M2-branes, and that it has a natural interpretation in loop space. We also formulate our Nahm equations using strong homotopy Lie algebras.

Chiral three-point interactions in 5 and 6 dimensions

We study N=(m,0) super-Poincare invariant six-dimensional massless and five-dimensional massive on-shell amplitudes. We demonstrate that in six dimensions, all possible three-point amplitudes involving tensor multiplets are necessarily embedded in gravitational theories. For non-gravitational amplitudes we consider instead five-dimensional massive amplitudes with N=(2,0) supersymmetry, aiming at describing the world volume theory of multiple M5 branes compactified on M^{4,1}x S^1. We find non-gravitational amplitudes whose on-shell degrees of freedom are shown to match those of the massive particle states that arise from self-dual strings wrapping a circle. Along the way we find interesting hints of a fermionic symmetry in the (2,0) theory, which accompanies the self-dual tensor gauge symmetry. We also discuss novel theories with (3,0) and (4,0) supersymmetry.

Non-abelian self-dual string solutions

We consider the equations of motion of the non-abelian 5-branes theory recently constructed in http://arxiv.org/abs/arXiv:1203.4224 and find exact string solutions both for uncompactified and compactified spacetime. Although one does not have the full supersymmetric construction of the non-abelian (2,0) theory, by combining knowledge of conformal symmetry and R-symmetry one can argue for the form of the 1/2 BPS equations in the case when only one scalar field is turned on. We solve this system and show that our string solutions could be lifted to become solutions of the non-abelian (2,0) theory with self-dual electric and magnetic charges, with the scalar field describing a M2-brane spike emerging out of the multiple M5-branes worldvolume.

A theory of non-abelian tensor gauge field with non-abelian gauge symmetry [formula omitted

The Chern–Simons action of the ABJM theory is not gauge invariant in the presence of a boundary. In Chu and Smith (2010) [1], this was shown to imply the existence of a Kac–Moody current algebra on the theory of multiple self-dual strings. In this paper we conjecture that the Kac–Moody symmetry induces a U(N)×U(N) gauge symmetry in the theory of N coincident M5-branes. As a start, we construct a G×G gauge symmetry algebra structure which naturally includes the tensor gauge transformation for a non-abelian 2-form tensor gauge field. The gauge covariant field strength is constructed. This new G×G gauge symmetry algebra allows us to write down a theory of a non-abelian tensor gauge field in any dimensions. The G×G gauge bosons can be either propagating, in which case the 2-form gauge fields would interact with each other through the 1-form gauge field; or they can be auxiliary and carry no local degrees of freedom, in which case the 2-form gauge fields would be self-interacting non-trivially. We finally comment on the possible application to the system of multiple M5-branes. We note that the field content of the G×G non-abelian tensor gauge theory can be fitted nicely into (1,0) supermultiplets; and we suggest a construction of the theory of multiple M5-branes with manifest (1,0) supersymmetry.

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.

Entropy of the self-dual string soliton

We compute the entropy and the corresponding central charge of the self-dual string soliton in the supergravity regime using the blackfold description of the fully localized M2-M5 intersection.

M-BRANE MODELS AND LOOP SPACES

I review an extension of the ADHMN construction of monopoles to M-brane models. This extended construction gives a map from solutions to the Basu–Harvey equation to solutions to the self-dual string equation transgressed to loop space. Loop spaces appear in fact quite naturally in M-brane models. This is demonstrated by translating a recently proposed M5-brane model to loop space. Finally, I comment on some recent developments related to the loop space approach to M-brane models.

Momentum modes of M5-branes in a 2d space

We study M5 branes by considering the selfdual strings parallel to a plane. With the internal oscillation frozen, each selfdual string gives a 5d SYM field. All selfdual strings together give a 6d field with 5 scalars, 3 gauge degrees of freedom and 8 fermionic degrees of freedom in adjoint representation of U(N). Selfdual strings with the same orientation have the SYM-type interaction. For selfdual strings with the different orientations, which could also be taken as the unparallel momentum modes of the 6d field on that plane or the (p,q) (r,s) strings on D3 with (p,q)\neq (r,s), the [i,j]+[j,k]\rightarrow [i,k] relation is not valid, so the coupling cannot be written in terms of the standard N \times N matrix multiplication. 3-string junction, which is the bound state of the unparallel [i,j] [j,k] selfdual strings, may play a role here.

M2-M5 blackfold funnels

Abstract We analyze the basic M2-M5 intersection in the supergravity regime using the blackfold approach. This approach allows us to recover the 1/4-BPS self-dual string soliton solution of Howe, Lambert and West as a three-funnel solution of an effective fivebrane worldvolume theory in a new regime, the regime of a large number of M2 and M5 branes. In addition, it allows us to discuss finite temperature effects for non-extremal self-dual string soliton solutions and wormhole solutions interpolating between stacks of M5 and anti-M5 branes. The purpose of this paper is to exhibit these solutions and their basic properties.

1/4BPS string junctions andN3problem in 6-dimensional (2,0) superconformal theories

We explore 1/4 BPS objects in the Coulomb phase of the ADE-type 6-dim (2,0) superconformal theories. By using the previous work on the junctions of strings in 5-dim gauge theories and 6-dim superconformal theories, we count the number of 1/4 BPS objects, which are made of waves on selfdual strings and junctions of selfdual strings and show that for all cases the number matches exactly one third of the anomaly constant $c_G=d_G h_G$ which is the product of dimension $d_G$ and dual Coxeter number $h_G$. This suggests the long sought after $N^3$ degrees of freedom are these 1/4 BPS objects at least in the Coulomb phase.

On instantons as Kaluza-Klein modes of M5-branes

Instantons and W-bosons in 5d maximally supersymmetric Yang-Mills theory arise from a circle compactification of the 6d (2,0) theory as Kaluza-Klein modes and winding self-dual strings, respectively. We study an index which counts BPS instantons with electric charges in Coulomb and symmetric phases. We first prove the existence of unique threshold bound state of (noncommutative) U(1) instantons for any instanton number, and also show that charged instantons in the Coulomb phase correctly give the degeneracy of SU(2) self-dual strings. By studying SU(N) self-dual strings in the Coulomb phase, we find novel momentum-carrying degrees on the worldsheet. The total number of these degrees equals the anomaly coefficient of SU(N) (2,0) theory. We finally show that our index can be used to study the symmetric phase of this theory, and provide an interpretation as the superconformal index of the sigma model on instanton moduli space.

Exact half-BPS string-junction solutions in six-dimensional supergravity

We construct SO(2,1) x SO(3)-invariant half-BPS solutions in six-dimensional (0,4) supergravity with m tensor multiplets. The space-time manifold of each one of these solutions consists of an AdS_2 x S^2 warped over a Riemann surface Sigma with boundary. The most general local solution is parametrized by one real harmonic function, and m+2 holomorphic functions which are subject to a quadratic constraint and a hermitian inequality, both of which are manifestly SO(2,m) invariant. Imposing suitable conditions on these harmonic and holomorphic functions, we construct globally regular supergravity solutions with N distinct AdS_3 x S^3 asymptotic regions and contractible Sigma. These solutions have an intricate moduli space, whose dimension equals 2(m+1)N -m-2 and matches the counting of three-form charge vectors and un-attracted scalars of the tensor multiplet. Exact explicit formulas for all supergravity fields are obtained in terms of the moduli. Our solutions give the near-horizon geometries for junctions of N self-dual strings in six dimensions, and are holographic duals to CFTs defined on N half-planes which share a common interface line. For m=5, the solutions lift to quarter-BPS solutions for six-dimensional (4,4) supergravity.

Constructing generalized self-dual strings

We generalize a recently developed ADHMN-like construction of self-dual string solitons using loop space. In particular, we present two extensions: The first one starts from solutions to the Basu-Harvey equation for the ABJM model, the second one starts from solutions to a corresponding BPS equation in an N=2 supersymmetric deformation of the BLG model. Both constructions yield solutions to the abelian and the nonabelian self-dual string equation transgressed to loop space. These equations might provide an effective description of M2-branes suspended between M5-branes.

Equivalence of the self-dual and Nambu-Goto strings

We establish explicitely the relation between the algebraic and Nambu-Goto strings when the target space is a four dimensional flat space. We find that the two theories are exactly equivalent only when the algebraic string is restricted to the self-dual or anti self-dual sectors. In its Hamiltonian formulation, the algebraic string defines a constrained system with first and second class constraints. In the self-dual case, we exhibit the appropriate set of second class constraints such that the resulting physical phase space is formulated in the same way as it is in the standard Nambu-Goto string. We conclude with a discussion on alternative quantisation schemes.

Constructing Self-Dual Strings

We present an ADHMN-like construction which generates self-dual string solutions to the effective M5-brane worldvolume theory from solutions to the Basu-Harvey equation. Our construction finds a natural interpretation in terms of gerbes, which we develop in some detail. We also comment on a possible extension to stacks of multiple M5-branes.