14 research outputs found
Abelian-Higgs and Vortices from ABJM: towards a string realization of AdS/CMT
We present ans\"{a}tze that reduce the mass-deformed ABJM model to gauged
Abelian scalar theories, using the fuzzy sphere matrices . One such
reduction gives a Toda system, for which we find a new type of nonabelian
vortex. Another gives the standard Abelian-Higgs model, thereby allowing us to
embed all the usual (multi-)vortex solutions of the latter into the ABJM model.
By turning off the mass deformation at the level of the reduced model, we can
also continuously deform to the massive theory in the massless ABJM
case. In this way we can embed the Landau-Ginzburg model into the AdS/CFT
correspondence as a consistent truncation of ABJM. In this context, the mass
deformation parameter and a field VEV act as and
respectively, leading to a well-motivated AdS/CMT construction from string
theory. To further this particular point, we propose a simple model for the
condensed matter field theory that leads to an approximate description for the
ABJM abelianization. Finally, we also find some BPS solutions to the
mass-deformed ABJM model with a spacetime interpretation as an M2-brane ending
on a spherical M5-brane.Comment: 43 pages, latex, explanations added in the introduction, end of
section 4, and on page 2
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 R^{2,1} x S^2 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 S^3 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.Comment: 60 pages, Latex; v2: references added; v3: typos corrected and
references adde
D-branes Wrapped on Fuzzy del Pezzo Surfaces
We construct classical solutions in quiver gauge theories on D0-branes
probing toric del Pezzo singularities in Calabi-Yau manifolds. Our solutions
represent D4-branes wrapped around fuzzy del Pezzo surfaces. We study the
fluctuation spectrum around the fuzzy CP^2 solution in detail. We also comment
on possible applications of our fuzzy del Pezzo surfaces to the fuzzy version
of F-theory, dubbed F(uzz) theory.Comment: 1+42 pages, 9 figures v2: references added v3: statements on the
structure of the Yukawa couplings weakened. published versio
Cartan-Weyl 3-algebras and the BLG Theory I: Classification of Cartan-Weyl 3-algebras
As Lie algebras of compact connected Lie groups, semisimple Lie algebras have
wide applications in the description of continuous symmetries of physical
systems. Mathematically, semisimple Lie algebra admits a Cartan-Weyl basis of
generators which consists of a Cartan subalgebra of mutually commuting
generators H_I and a number of step generators E^\alpha that are characterized
by a root space of non-degenerate one-forms \alpha. This simple decomposition
in terms of the root space allows for a complete classification of semisimple
Lie algebras. In this paper, we introduce the analogous concept of a
Cartan-Weyl Lie 3-algebra. We analyze their structure and obtain a complete
classification of them. Many known examples of metric Lie 3-algebras (e.g. the
Lorentzian 3-algebras) are special cases of the Cartan-Weyl 3-algebras. Due to
their elegant and simple structure, we speculate that Cartan-Weyl 3-algebras
may be useful for describing some kinds of generalized symmetries. As an
application, we consider their use in the Bagger-Lambert-Gustavsson (BLG)
theory.Comment: LaTeX. 34 pages.v2. deleted some distracting paragraphs in the
introduction to bring more out the main results of the paper. typos corrected
and references adde
The unwarped, resolved, deformed conifold: fivebranes and the baryonic branch of the Klebanov-Strassler theory
We study a gravity solution corresponding to fivebranes wrapped on the
of the resolved conifold. By changing a parameter the solution continuously
interpolates between the deformed conifold with flux and the resolved conifold
with branes. Therefore, it displays a geometric transition, purely in the
supergravity context. The solution is a simple example of torsional geometry
and may be thought of as a non-K\"ahler analog of the conifold. By U-duality
transformations we can add D3 brane charge and recover the solution in the form
originally derived by Butti et al. This describes the baryonic branch of the
Klebanov-Strassler theory. Far along the baryonic branch the field theory gives
rise to a fuzzy two-sphere. This corresponds to the D5 branes wrapping the
two-sphere of the resolved conifold in the gravity solution.Comment: 41 pages, 7 figure
Causal structures and causal boundaries
We give an up-to-date perspective with a general overview of the theory of
causal properties, the derived causal structures, their classification and
applications, and the definition and construction of causal boundaries and of
causal symmetries, mostly for Lorentzian manifolds but also in more abstract
settings.Comment: Final version. To appear in Classical and Quantum Gravit