2,728 research outputs found
FRW and domain walls in higher spin gravity
We present exact solutions to Vasiliev's bosonic higher spin gravity
equations in four dimensions with positive and negative cosmological constant
that admit an interpretation in terms of domain walls, quasi-instantons and
Friedman-Robertson-Walker (FRW) backgrounds. Their isometry algebras are
infinite dimensional higher-spin extensions of spacetime isometries generated
by six Killing vectors. The solutions presented are obtained by using a method
of holomorphic factorization in noncommutative twistor space and gauge
functions. In interpreting the solutions in terms of Fronsdal-type fields in
spacetime, a field-dependent higher spin transformation is required, which is
implemented at leading order. To this order, the scalar field solves
Klein-Gordon equation with conformal mass in (anti) de Sitter space. We
interpret the FRW solution with de Sitter asymptotics in the context of
inflationary cosmology and we expect that the domain wall and FRW solutions are
associated with spontaneously broken scaling symmetries in their holographic
description. We observe that the factorization method provides a convenient
framework for setting up a perturbation theory around the exact solutions, and
we propose that the nonlinear completion of particle excitations over FRW and
domain wall solutions requires black hole-like states.Comment: 63 page
Dirichlet sigma models and mean curvature flow
The mean curvature flow describes the parabolic deformation of embedded
branes in Riemannian geometry driven by their extrinsic mean curvature vector,
which is typically associated to surface tension forces. It is the gradient
flow of the area functional, and, as such, it is naturally identified with the
boundary renormalization group equation of Dirichlet sigma models away from
conformality, to lowest order in perturbation theory. D-branes appear as fixed
points of this flow having conformally invariant boundary conditions. Simple
running solutions include the paper-clip and the hair-pin (or grim-reaper)
models on the plane, as well as scaling solutions associated to rational (p, q)
closed curves and the decay of two intersecting lines. Stability analysis is
performed in several cases while searching for transitions among different
brane configurations. The combination of Ricci with the mean curvature flow is
examined in detail together with several explicit examples of deforming curves
on curved backgrounds. Some general aspects of the mean curvature flow in
higher dimensional ambient spaces are also discussed and obtain consistent
truncations to lower dimensional systems. Selected physical applications are
mentioned in the text, including tachyon condensation in open string theory and
the resistive diffusion of force-free fields in magneto-hydrodynamics.Comment: 77 pages, 21 figure
BMN Operators for N=1 Superconformal Yang-Mills Theories and Associated String Backgrounds
We study a class of near-BPS operators for a complex 2-parameter family of
N=1 superconformal Yang-Mills theories that can be obtained by a
Leigh-Strassler deformation of N=4 SYM theory. We identify these operators in
the large N and large R-charge limit and compute their exact scaling dimensions
using N=1 superspace methods. From these scaling dimensions we attempt to
reverse-engineer the light-cone worldsheet theory that describes string
propagation on the Penrose limit of the dual geometry.Comment: 47 pages, 1 figure, 1 table; v2 a few typos corrected; v3 added
acknowledgements, a reference and improved discussion in section
Noncommutative Electromagnetism As A Large N Gauge Theory
We map noncommutative (NC) U(1) gauge theory on R^d_C X R^{2n}_{NC} to U(N ->
\infty) Yang-Mills theory on R^d_C, where R^d_C is a d-dimensional commutative
spacetime while R^{2n}_{NC} is a 2n-dimensional NC space. The resulting U(N)
Yang-Mills theory on R^d_C is equivalent to that obtained by the dimensional
reduction of (d+2n)-dimensional U(N) Yang-Mills theory onto R^d_C. We show that
the gauge-Higgs system (A_\mu,\Phi^a) in the U(N -> \infty) Yang-Mills theory
on R^d_C leads to an emergent geometry in the (d+2n)-dimensional spacetime
whose metric was determined by Ward a long time ago. In particular, the
10-dimensional gravity for d=4 and n=3 corresponds to the emergent geometry
arising from the 4-dimensional N=4 vector multiplet in the AdS/CFT duality. We
further elucidate the emergent gravity by showing that the gauge-Higgs system
(A_\mu,\Phi^a) in half-BPS configurations describes self-dual Einstein gravity.Comment: 25 pages; More clarifications, to appear in Eur. Phys. J.
Complete Supersymmetric Quantum Mechanics of Magnetic Monopoles in N=4 SYM Theory
We find the most general low energy dynamics of 1/2 BPS monopoles in the N=4
supersymmetric Yang-Mills theories (SYM) when all six adjoint Higgs expectation
values are turned on. When only one Higgs is turned on, the Lagrangian is
purely kinetic. When all six are turned on, however, this moduli space dynamics
is augmented by five independent potential terms, each in the form of half the
squared norm of a Killing vector field on the moduli space. A generic
stationary configuration of the monopoles can be interpreted as stable non BPS
dyons, previously found as non-planar string webs connecting D3-branes. The
supersymmetric extension is also found explicitly, and gives the complete
quantum mechanics of monopoles in N=4 SYM theory. We explore its supersymmetry
algebra.Comment: Errors in the SUSY algebra corrected. The version to appear in PR
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