38 research outputs found
Dimensional reduction of the ABJM model
We dimensionally reduce the ABJM model, obtaining a two-dimensional theory
that can be thought of as a 'master action'. This encodes information about
both T- and S-duality, i.e. describes fundamental (F1) and D-strings (D1) in 9
and 10 dimensions. The Higgsed theory at large VEV and large k yields D1-brane
actions in 9d and 10d, depending on which auxiliary fields are integrated out.
For N=1 there is a map to a Green-Schwarz string wrapping a nontrivial circle
in C^4/Z_k.Comment: 23 pages, Latex; v2: added some clarifying comments on the action of
T-duality in Section 2.1.
Bifundamental Fuzzy 2-Sphere and Fuzzy Killing Spinors
We review our construction of a bifundamental version of the fuzzy 2-sphere
and its relation to fuzzy Killing spinors, first obtained in the context of the
ABJM membrane model. This is shown to be completely equivalent to the usual
(adjoint) fuzzy sphere. We discuss the mathematical details of the
bifundamental fuzzy sphere and its field theory expansion in a
model-independent way. We also examine how this new formulation affects the
twisting of the fields, when comparing the field theory on the fuzzy sphere
background with the compactification of the 'deconstructed' (higher
dimensional) field theory.Comment: Invited contribution to special issue of SIGMA (Symmetry,
Integrability and Geometry: Methods and Applications) "Noncommutative Spaces
and Fields
Multiple Membranes in M-theory
We review developments in the theory of multiple, parallel membranes in
M-theory. After discussing the inherent difficulties pertaining to a maximally
supersymmetric lagrangian formulation with the appropriate field content and
symmetries, we discuss how introducing the concept of 3-algebras allows 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
describe how these are equivalent to a type of conventional superconformal
Chern-Simons gauge theories at level k, coupled to bifundamental matter.
Analysing the physical properties of these theories leads to the identification
of a certain subclass of models with configurations of M2-branes in Z_k
orbifolds of M-theory. In addition these models give rise to a whole new sector
of the gauge/gravity duality in the form of an AdS_4/CFT_3 correspondence. We
also discuss mass deformations, higher derivative corrections as well as the
possibility of extracting information about M5-brane physics.Comment: 180 pages, 3 figures, Latex; v2: various typos corrected,
clarifications, references and acknowledgements added, title modified,
submitted to Physics Report
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.Comment: 1+11 pages, Latex; v2: section 3 revised and references adde
6D (2,0) Bootstrap with soft-Actor-Critic
We study numerically the 6D (2,0) superconformal bootstrap using the
soft-Actor-Critic (SAC) algorithm as a stochastic optimizer. We focus on the
four-point functions of scalar superconformal primaries in the energy-momentum
multiplet. Starting from the supergravity limit, we perform searches for
adiabatically varied central charges and derive two curves for a collection of
80 CFT data (70 of these data correspond to unprotected long multiplets and 10
to protected short multiplets). We conjecture that the two curves capture the
A- and D-series (2,0) theories. Our results are competitive when compared to
the existing bounds coming from standard numerical bootstrap methods, and data
obtained using the OPE inversion formula. With this paper we are also releasing
our Python implementation of the SAC algorithm, BootSTOP. The paper discusses
the main functionality features of this package.Comment: 30 pages, 10 figures; v2: references adde
Relating U(N)xU(N) to SU(N)xSU(N) Chern-Simons Membrane theories
By integrating out the U(1)_B gauge field, we show that the U(n)xU(n) ABJM
theory at level k is equivalent to a Z_k identification of the
(SU(n)xSU(n))/Z_n Chern-Simons theory, but only when n and k are coprime. As a
consequence, the k=1 ABJM model for two M2-branes in R^8 can be identified with
the N=8 (SU(2)xSU(2))/Z_2 theory. We also conjecture that the U(2)xU(2) ABJM
model at k=2 is equivalent to the N=8 SU(2)xSU(2)-theory.Comment: 16 pages, Latex; v2: references added; v3: Clarifications adde
M2 to D2
We examine the recently proposed "3-algebra" field theory for multiple M2-branes and show that when a scalar field valued in the 3-algebra develops a vacuum expectation value, the resulting Higgs mechanism has the novel effect of promoting topological (Chern-Simons) to dynamical (Yang-Mills) gauge fields. This leads to a precise derivation of the maximally supersymmetric Yang-Mills theory on multiple D2-branes and thereby provides a relationship between 3-algebras and Yang-Mills theories. We discuss the physical interpretation of this result
M2-branes on M-folds
We argue that the moduli space for the Bagger-Lambert A_4 theory at level k
is (R^8 \times R^8)/D_{2k}, where D_{2k} is the dihedral group of order 4k. We
conjecture that the theory describes two M2-branes on a Z_{2k} ``M-fold'', in
which a geometrical action of Z_{2k} is combined with an action on the branes.
For k=1, this arises as the strong coupling limit of two D2-branes on an O2^-
orientifold, whose worldvolume theory is the maximally supersymmetric SO(4)
gauge theory. Finally, in an appropriate large-k limit we show that one
recovers compactified M-theory and the M2-branes reduce to D2-branes.Comment: 16 pages, LaTeX, v2: typos corrected, included appendices on
Chern-Simons level quantization and monopole charge quantizatio