We study the holographic field theory dual of a probe SU(2) Yang-Mills field in a background (4 + 1)-dimensional asymptotically Anti-de Sitter space. We find a new ground state when a magnetic component of the gauge field is larger than a critical value. The ground state forms a triangular Abrikosov lattice in the spatial directions perpendicular to the magnetic field. The lattice is composed of superconducting vortices induced by the condensation of a charged vector operator. We perform this calculation both at finite temperature and at zero temperature with a hard wall cutoff dual to a confining gauge theory. The study of this state may be of relevance to both holographic condensed matter models as well as to heavy ion physics. The results shown here provide support for the proposal that such a ground state may be found in the QCD vacuum when a large magnetic field is present.

Magnetic field induced lattice ground states from holography

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.

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

We develop semistrict higher gauge theory fromrst principles. In particular, we describe the dierential Deligne cohomology underlying semistrict principal 2-bundles with connective structures. Principal 2-bundles are obtained in terms of weak 2-functors from the � Cech groupoid to weak Lie 2-groups. As is demonstrated, some of these Lie 2-groups can be dierentiated to semistrict Lie 2-algebras by a method due to � We further derive the full description of connective structures on semistrict principal 2- bundles including the non-linear gauge transformations. As an application, we use a twistor construction to derive superconformal constraint equations in six dimensions for a non- AbelianN = (2; 0) tensor multiplet taking values in a semistrict Lie 2-algebra.

/pdf/semistrict-higher-gauge-theory-1avrz732ho.pdf

Semistrict higher gauge theory

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. We thus arrive at the non-Abelian differential cohomology that describes principal 3-bundles with connective structure.

With the aim to study six-dimensional (2, 0) superconformal theories with non-Abelian tensor multiplets we propose a five-dimensional superconformal action with eight supersymmetries for an infinite tower of non-Abelian vector, tensor and hypermultiplets. It describes the dynamics of the complete spectrum of the (2, 0) theories compactified on a circle coupled to an additional vector multiplet containing the circle radius and the Kaluza-Klein vector arising from the six-dimensional metric. All couplings are only given in terms of group theoretical constants and the Kaluza-Klein levels. After superconformal symmetry is reduced to Poincare supersymmetry we find a Kaluza-Klein inspired action coupling super-Yang-Mills theory to an infinite tower of massive non-Abelian tensors. We explore the possibility to restore sixteen supersymmetries by using techniques known from harmonic superspace. Namely, additional bosonic coordinates on a four-sphere are introduced to enhance the R-symmetry group. Maximally supersymmetric Yang-Mills theories and the Abelian (2, 0) tensor theories are recovered as special cases of our construction. Finally, we comment on the generation of an anomaly balancing Wess-Zumino term for the R-symmetry vector at one loop.

Non-Abelian tensor towers and (2,0) superconformal theories

We construct an alternative form of the M5-brane action in which the sixdimensional worldvolume is subject to a covariant split into 3+3 directions by a triplet of auxiliary fields. We consider the relation of this action to the original form of the M5-brane action and to a Nambu-Poisson 5-brane action based on the Bagger-Lambert-Gustavsson model with the gauge symmetry of volume preserving diffeomorphisms.

The M5-brane action revisited

We consider the equations of motion of the non-abelian 5-branes theory recently constructed in [
 1
 ] 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.

Non-Abelian Self-Dual String Solutions

We consider the non-abelian theory [1] 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 [2] 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.

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

In this work, we extend a theory which describes a linearly self-dual exact 3-form field in six dimensional spacetime within the formalism of arXiv:1511.08220 and arXiv:1903.12196 to an action which fully describes an M5-brane in the eleven-dimensional supergravity background. The action we obtain has all the required symmetries including kappa-symmetry. Although the derivation of the action and the proof the symmetries do not require one to express the action explicitly in terms of the original field contents, we also give an initial attempt to give this expression.

/pdf/covariant-m5-brane-action-with-self-dual-3-form-qsbf9tg7u6.pdf

Covariant M5-brane action with self-dual 3-form

We present an attempt to formulate an action for the worldvolume theory of a single M5-brane, based on the splitting of the six worldvolume directions into 2+4, which breaks manifest Lorentz invariance from SO(1, 5) to SO(1, 1) × SO(4). To this end, an action for the free six-dimensional (2,0) chiral tensor multiplet, and separately, a nonlinearly interacting chiral 2-form action are constructed. By studying the Lagrangian formulation for the chiral 2-form with 2+4 splitting, it is suggested that, if exists, the modified diffeomorphism of the theory on curved six-dimensional space-time is less trivial than its 1+5 and 3+3 counterpart, thus hindering the coupling of the chiral 2-form to the induced metric on the worldvolume of the M5-brane. We discuss difficulties of further generalisation of the theory. Finally, in terms of Hamiltonian analysis, we show that the naively gauge-fixed failed-PST-covariantised Lagrangian has the correct number of degrees of freedom, and satisfies the hyper-surface deformation algebra.

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Pichet Vanichchapongjaroen

Papers

The M5-brane action revisited

Non-Abelian Self-Dual String Solutions

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

Covariant M5-brane action with self-dual 3-form

Towards 2+4 formulation of M5-brane.