Constantinos Papageorgakis

D2 to D2

Starting from maximally supersymmetric (2+1)d Yang-Mills theory and using a duality transformation due to de Wit, Nicolai and Samtleben, we obtain the ghost-free Lorentzian 3-algebra theory that has recently been proposed to describe M2-branes. Our derivation does not invoke any properties of 3-algebras. Being derivable from SYM, the final theory is manifestly equivalent to it on-shell and should not be thought of as the IR limit that describes M2-branes, though it does have enhanced R-symmetry as well as superconformal symmetry off-shell.

M5-Branes, D4-Branes and quantum 5D super-Yang-Mills

We revisit the relation of the six-dimensional (2, 0) M5-brane Conformal Field Theory compactified on S1 to 5D maximally supersymmetric Yang-Mills Gauge Theory. We show that in the broken phase 5D super-Yang-Mills contains a spectrum of soliton states that can be identified with the complete Kaluza-Klein modes of an M2-brane ending on the M5-branes. This provides evidence that the (2, 0) theory on S1 is equivalent to 5D super-Yang-Mills with no additional UV degrees of freedom, suggesting that the latter is in fact a well-defined quantum theory and possibly finite.

Nonabelian (2,0) tensor multiplets and 3-algebras

Using 3-algebras we obtain a nonabelian system of equations that furnish a representation of the (2, 0)-supersymmetric tensor multiplet. The on-shell conditions are quite restrictive so that the system can be reduced to five-dimensional gauge theory along with six-dimensional abelian (2, 0) tensor multiplets. We briefly discuss possible applications to D4-branes using a spacelike reduction and M5-branes using a null reduction.

Multiple Membranes in M-theory

We review developments in the theory of multiple, parallel membranes in M-theory. After discussing the inherent diffi culties with constructing a maximally supersymmetric lagrangian with the appropriate field content and symmetries, we introduce 3-algebras and show how they allow for such a description. Different choices of 3-algebras lead to distinct classes of 2+1 dimensional theories with varying degrees of supersymmetry. We then demonstrate that these theories are equivalent to conventional superconformal Chern-Simons gauge theories at level k, but with bifundamental matter. Analysing the physical properties of these theories leads to the identification of a certain sub class of models with configurations of M2-branes on Zk orbifolds. These models give rise to a whole new gauge/gravity duality in the form of an AdS4/CFT3 correspondence. We also discuss mass deformations, higher derivative corrections, and the possibility of extracting information about M5-brane physics.

The fuzzy S 2 structure of M2-M5 systems in ABJM membrane theories

We analyse the fluctuations of the ground-state/funnel solutions proposed to describe M2-M5 systems in the level-k mass-deformed/pure Chern-Simons-matter ABJM theory of multiple membranes. We show that in the large N limit the fluctuations approach the space of functions on the 2-sphere rather than the naively expected 3-sphere. This is a novel realisation of the fuzzy 2-sphere in the context of Matrix Theories, which uses bifundamental instead of adjoint scalars. Starting from the multiple M2-brane action, a U(1) Yang-Mills theory on 2,1 × S2 is recovered at large N, which is consistent with a single D4-brane interpretation in Type IIA string theory. This is as expected at large k, where the semiclassical analysis is valid. Several aspects of the fluctuation analysis, the ground-state/funnel solutions and the mass-deformed/pure ABJM equations can be understood in terms of a discrete noncommutative realisation of the Hopf fibration. We discuss the implications for the possibility of finding an M2-brane worldvolume derivation of the classical S3 geometry of the M2-M5 system. Using a rewriting of the equations of the SO(4)-covariant fuzzy 3-sphere construction, we also directly compare this fuzzy 3-sphere against the ABJM ground-state/funnel solutions and show them to be different.

Relating U(N) × U(N) to SU(N) × SU(N) Chern-Simons membrane theories

By integrating out the U(1)B gauge field, we show that the U(n) × U(n) ABJM theory at level k is equivalent to a

Constraints on chiral operators in N = 2 SCFTs

{\mathbb{Z}_k}

Argyres-Douglas Theories and S-Duality

identification of the

Higgsing M2 to D2 with gravity: N=6 chiral supergravity from topologically gauged ABJM theory

{{\left( {{\text{SU}}(n) \times {\text{SU}}(n)} \right)} \mathord{\left/{\vphantom {{\left( {{\text{SU}}(n) \times {\text{SU}}(n)} \right)} {{\mathbb{Z}_n}}}} \right.} {{\mathbb{Z}_n}}}

The power of the Higgs mechanism: higher-derivative BLG theories

Chern-Simons theory, but only when n and k are coprime. As a consequence, the k = 1 ABJM model for two M2-branes in