1,134 research outputs found
Higher su(N) tensor products
We extend our recent results on ordinary su(N) tensor product multiplicities
to higher su(N) tensor products. Particular emphasis is put on four-point
couplings where the tensor product of four highest weight modules is
considered. The number of times the singlet occurs in the decomposition is the
associated multiplicity. In this framework, ordinary tensor products correspond
to three-point couplings. As in that case, the four-point multiplicity may be
expressed explicitly as a multiple sum measuring the discretised volume of a
convex polytope. This description extends to higher-point couplings as well. We
also address the problem of determining when a higher-point coupling exists,
i.e., when the associated multiplicity is non-vanishing. The solution is a set
of inequalities in the Dynkin labels.Comment: 17 pages, LaTe
Black Hole Production from High Energy Scattering in AdS/CFT
In this article we show how to set up initial states in SYM
theory that correspond to high energy graviton collisions, leading to black
hole formation in . For this purpose, we study states in the
gauge theory that are dual to graviton wavepackets localized at the center of
, and carrying large angular momentum along the . These states are
created by exciting only the s-wave mode of one of the complex adjoint scalars
of SYM. For a single graviton, the state is 1/2 BPS and one can show that it is
dual to a linearized 1/2 BPS geometry in the bulk. Exploiting this dictionary,
we show how to localize the particle's wavefunciton so that the dual linearized
metric has the form of a Aichelburg-Sexl shock wave. One can then put two such
shock waves into a head-on collision, which is known to produce a trapped
surface. Finally, we discuss the prospect of studying graviton scattering
directly at strong coupling in the gauge theory using a reduced model of matrix
quantum mechanics.Comment: 11 pages, revtex format, no figure
Multi-matrix models and emergent geometry
Encouraged by the AdS/CFT correspondence, we study emergent local geometry in
large N multi-matrix models from the perspective of a strong coupling
expansion. By considering various solvable interacting models we show how the
emergence or non-emergence of local geometry at strong coupling is captured by
observables that effectively measure the mass of off-diagonal excitations about
a semiclassical eigenvalue background. We find emergent geometry at strong
coupling in models where a mass term regulates an infrared divergence. We also
show that our notion of emergent geometry can be usefully applied to fuzzy
spheres. Although most of our results are analytic, we have found numerical
input valuable in guiding and checking our results.Comment: 1+34 pages, 4 figures. References adde
Strings on conifolds from strong coupling dynamics, part I
A method to solve various aspects of the strong coupling expansion of the
superconformal field theory duals of AdS_5 x X geometries from first principles
is proposed. The main idea is that at strong coupling the configurations that
dominate the low energy dynamics of the field theory compactified on a three
sphere are given by certain non-trivial semi-classical configurations in the
moduli space of vacua.
We show that this approach is self-consistent and permits one to express most
of the dynamics in terms of an effective N=4 SYM dynamics. This has the
advantage that some degrees of freedom that move the configurations away from
moduli space can be treated perturbatively, unifying the essential low energy
dynamics of all of these theories. We show that with this formalism one can
compute the energies of strings in the BMN limit in the Klebanov-Witten theory
from field theory considerations, matching the functional form of results found
using AdS geometry. This paper also presents various other technical results
for the semiclassical treatment of superconformal field theories.Comment: 52 pages, JHEP3 styl
Aspects of ABJM orbifolds with discrete torsion
We analyze orbifolds with discrete torsion of the ABJM theory by a finite
subgroup of . Discrete torsion is implemented by
twisting the crossed product algebra resulting after orbifolding. It is shown
that, in general, the order of the cocycle we chose to twist the algebra by
enters in a non trivial way in the moduli space. To be precise, the M-theory
fiber is multiplied by a factor of in addition to the other effects that
were found before in the literature. Therefore we got a
action on the fiber. We present a general
analysis on how this quotient arises along with a detailed analysis of the
cases where is abelian
Logarithmic correction to scaling for multi-spin strings in the AdS_5 black hole background
We find new explicit solutions describing closed strings spinning with equal
angular momentum in two independent planes in the black hole spacetime.
These are folded strings in the radial direction and also winding
times around an angular direction. We especially consider these solutions in
the long string and high temperature limit, where it is shown that there is a
logarithmic correction to the scaling between energy and spin. This is similar
to the one-spin case. The strings are spinning, or actually orbiting around the
black hole of the black hole spacetime, similarly to solutions
previously found in black hole spacetimes.Comment: 11 pages, Final version, To appear in IJMP
Open string axions and the flavor problem
We consider extensions of the standard model inspired by intersecting D-brane
constructions, in order to address flavor mass textures. We include additional
anomalous gauge symmetries, and scalar fields to break them and to generate
Froggatt-Nielsen mass terms. Green-Schwarz axions are included to cancel mixed
anomalies rendering the models consistent. At low energies, a residual
anomalous global symmetry remains, and its associated pseudo-Goldstone mode
becomes the physical axion, which can be interpreted as an axion arising from
open string modes. General considerations show that such axions are very common
in D-brane models and can be completely incompatible with current bounds.
Astrophysical constraints are placed on the axion both by including neutrino
masses in the Froggatt-Nielsen scheme and considering QCD instanton
contributions to the axion mass. We find simple models where the axion decay
constant is in the allowed range, but only one such minimal model with this
property is free from excessive fine tunings elsewhere. We also note that
generically addressing flavor textures for the CKM matrix leads to
deconstructed extra dimensions.Comment: 30 pages, 2 figures. v2: references added. v3:typos fixe
A study of open strings ending on giant gravitons, spin chains and integrability
We systematically study the spectrum of open strings attached to half BPS
giant gravitons in the N=4 SYM AdS/CFT setup. We find that some null
trajectories along the giant graviton are actually null geodesics of AdS_5x
S^5, so that we can study the problem in a plane wave limit setup. We also find
the description of these states at weak 't Hooft coupling in the dual CFT. We
show how the dual description is given by an open spin chain with variable
number of sites. We analyze this system in detail and find numerical evidence
for integrability. We also discover an interesting instability of long open
strings in Ramond-Ramond backgrounds that is characterized by having a
continuum spectrum of the string, which is separated from the ground state by a
gap. This instability arises from accelerating the D-brane on which the strings
end via the Ramond-Ramond field. From the integrable spin chain point of view,
this instability prevents us from formulating the integrable structure in terms
of a Bethe Ansatz construction.Comment: 38 pages+appendices, 9 figures. Uses JHEP3. v2: added reference
A Monte-Carlo study of the AdS/CFT correspondence: an exploration of quantum gravity effects
In this paper we study the AdS/CFT correspondence for N=4 SYM with gauge
group U(N), compactified on S^3 in four dimensions using Monte-Carlo
techniques. The simulation is based on a particular reduction of degrees of
freedom to commuting matrices of constant fields, and in particular, we can
write the wave functions of these degrees of freedom exactly. The square of the
wave function is equivalent to a probability density for a Boltzman gas of
interacting particles in six dimensions. From the simulation we can extract the
density particle distribution for each wave function, and this distribution can
be interpreted as a special geometric locus in the gravitational dual. Studying
the wave functions associated to half-BPS giant gravitons, we are able to show
that the matrix model can measure the Planck scale directly. We also show that
the output of our simulation seems to match various theoretical expectations in
the large N limit and that it captures 1/N effects as statistical fluctuations
of the Boltzman gas with the expected scaling. Our results suggest that this is
a very promising approach to explore quantum corrections and effects in
gravitational physics on AdS spaces.Comment: 40 pages, 7 figures, uses JHEP. v2: references adde
Mass-Gaps and Spin Chains for (Super) Membranes
We present a method for computing the non-perturbative mass-gap in the theory
of Bosonic membranes in flat background spacetimes with or without background
fluxes. The computation of mass-gaps is carried out using a matrix
regularization of the membrane Hamiltonians. The mass gap is shown to be
naturally organized as an expansion in a 'hidden' parameter, which turns out to
be : d being the related to the dimensionality of the background
space. We then proceed to develop a large perturbation theory for the
membrane/matrix-model Hamiltonians around the quantum/mass corrected effective
potential. The same parameter that controls the perturbation theory for the
mass gap is also shown to control the Hamiltonian perturbation theory around
the effective potential. The large perturbation theory is then translated
into the language of quantum spin chains and the one loop spectra of various
Bosonic matrix models are computed by applying the Bethe ansatz to the one-loop
effective Hamiltonians for membranes in flat space times. Apart from membranes
in flat spacetimes, the recently proposed matrix models (hep-th/0607005) for
non-critical membranes in plane wave type spacetimes are also analyzed within
the paradigm of quantum spin chains and the Bosonic sectors of all the models
proposed in (hep-th/0607005) are diagonalized at the one-loop level.Comment: 36 Page
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