14,292 research outputs found
Noncommutative field theories on : Towards UV/IR mixing freedom
We consider the noncommutative space , a deformation of
the algebra of functions on which yields a "foliation" of
into fuzzy spheres. We first construct a natural matrix base
adapted to . We then apply this general framework to the
one-loop study of a two-parameter family of real-valued scalar noncommutative
field theories with quartic polynomial interaction, which becomes a non-local
matrix model when expressed in the above matrix base. The kinetic operator
involves a part related to dynamics on the fuzzy sphere supplemented by a term
reproducing radial dynamics. We then compute the planar and non-planar 1-loop
contributions to the 2-point correlation function. We find that these diagrams
are both finite in the matrix base. We find no singularity of IR type, which
signals very likely the absence of UV/IR mixing. We also consider the case of a
kinetic operator with only the radial part. We find that the resulting theory
is finite to all orders in perturbation expansion.Comment: 31 pages, 4 figures. Improved version. Sections 5.1 and 5.2 have been
clarified. A minor error corrected. References adde
Membranes, Strings and Integrability
In the first half of this note, after briefly motivating and reviewing
membrane field theories, we consider their BPS funnel solutions. We discuss
some aspects of embedding M-theory fuzzy funnels in these theories. In the
second half, we focus on ABJM theory and explain a test of AdS4/CFT3 based on
integrability. We discuss a numerical mismatch at one loop in worldsheet
perturbation theory and its possible resolutions.Comment: 6 pages, contribution to the proceedings of the 4th RTN meeting,
Varna, Bulgaria, to be published in Fortschritte der Physik; v2,3: references
adde
Membranes on Calibrations
M2-branes can blow up into BPS funnels that end on calibrated intersections
of M5-branes. In this quick note, we make the observation that the constraints
required for the consistency of these solutions are automatic in
Bagger-Lambert-Gustavsson (BLG) theory, thanks to the fundamental identity and
the supersymmetry of the calibration. We use this to explain how the previous
ad hoc fuzzy funnel constructions emerge in this picture, and make some
comments about the role of the 3-algebra trace form in the derivation.Comment: 9 pages, no figures; references added, minor change
Non-commutative World-volume Geometries: Branes on SU(2) and Fuzzy Spheres
The geometry of D-branes can be probed by open string scattering. If the
background carries a non-vanishing B-field, the world-volume becomes
non-commutative. Here we explore the quantization of world-volume geometries in
a curved background with non-zero Neveu-Schwarz 3-form field strength H = dB.
Using exact and generally applicable methods from boundary conformal field
theory, we study the example of open strings in the SU(2) Wess-Zumino-Witten
model, and establish a relation with fuzzy spheres or certain (non-associative)
deformations thereof. These findings could be of direct relevance for D-branes
in the presence of Neveu-Schwarz 5-branes; more importantly, they provide
insight into a completely new class of world-volume geometries.Comment: 19 pages, LaTeX, 1 figure; some explanations improved, references
adde
Holographic Entanglement in a Noncommutative Gauge Theory
In this article we investigate aspects of entanglement entropy and mutual
information in a large-N strongly coupled noncommutative gauge theory, both at
zero and at finite temperature. Using the gauge-gravity duality and the
Ryu-Takayanagi (RT) prescription, we adopt a scheme for defining spatial
regions on such noncommutative geometries and subsequently compute the
corresponding entanglement entropy. We observe that for regions which do not
lie entirely in the noncommutative plane, the RT-prescription yields sensible
results. In order to make sense of the divergence structure of the
corresponding entanglement entropy, it is essential to introduce an additional
cut-off in the theory. For regions which lie entirely in the noncommutative
plane, the corresponding minimal area surfaces can only be defined at this
cut-off and they have distinctly peculiar properties.Comment: 28 pages, multiple figures; minor changes, conclusions unchange
Brane Dynamics in Background Fluxes and Non-commutative Geometry
Branes in non-trivial backgrounds are expected to exhibit interesting
dynamical properties. We use the boundary conformal field theory approach to
study branes in a curved background with non-vanishing Neveu-Schwarz 3-form
field strength. For branes on an , the low-energy effective action is
computed to leading order in the string tension. It turns out to be a field
theory on a non-commutative `fuzzy 2-sphere' which consists of a Yang-Mills and
a Chern-Simons term. We find a certain set of classical solutions that have no
analogue for flat branes in Euclidean space. These solutions show, in
particular, how a spherical brane can arise as bound state from a stack of
D0-branes.Comment: 25 page
Non-Abelian BIonic Brane Intersections
We study "fuzzy funnel" solutions to the non-Abelian equations of motion of
the D-string. Our funnel describes n^6/360 coincident D-strings ending on n^3/6
D7-branes, in terms of a fuzzy six-sphere which expands along the string. We
also provide a dual description of this configuration in terms of the world
volume theory of the D7-branes. Our work makes use of an interesting non-linear
higher dimensional generalization of the instanton equations.Comment: 17 pages uses harvmac; v2: small typos corrected, refs adde
Giant Gravitons in Conformal Field Theory
Giant gravitons in AdS_5 x S^5, and its orbifolds, have a dual field theory
representation as states created by chiral primary operators. We argue that
these operators are not single-trace operators in the conformal field theory,
but rather are determinants and subdeterminants of scalar fields; the stringy
exclusion principle applies to these operators. Evidence for this
identification comes from three sources: (a) topological considerations in
orbifolds, (b) computation of protected correlators using free field theory and
(c) a Matrix model argument. The last argument applies to AdS_7 x S^4 and the
dual (2,0) theory, where we use algebraic aspects of the fuzzy 4-sphere to
compute the expectation value of a giant graviton operator along the Coulomb
branch of the theory.Comment: 37 pages, LaTeX, 1 figure. v2: references and acknowledgements added,
small correction
- …