20 research outputs found
A toy model for the AdS/CFT correspondence
We study the large N gauged quantum mechanics for a single Hermitian matrix
in the Harmonic oscillator potential well as a toy model for the AdS/CFT
correspondence. We argue that the dual geometry should be a string in two
dimensions with a curvature of stringy size. Even though the dual geometry is
not weakly curved, one can still gain knowledge of the system from a detailed
study of the open-closed string duality. We give a mapping between the basis of
states made of traces (closed strings) and the eigenvalues of the matrix
(D-brane picture) in terms of Schur polynomials. We connect this model with the
study of giant gravitons in AdS_5 x S^5. We show that the two giant gravitons
that expand along AdS_5 and S^5 can be interpreted in the matrix model as
taking an eigenvalue from the Fermi sea and exciting it very much, or as making
a hole in the Fermi sea respectively. This is similar to recent studies of the
c=1 string. This connection gives new insight on how to perform calculations
for giant gravitons.Comment: 19 pages JHEP, 4 figures. v2: comments added, typos fixed, additional
refs. v3: The paper has been largely revised, to make the relation as a limit
of N=4 SYM clear, also some proofs have been written in full rather than
sketched. This updated version reflects the changes that were made in the
published versio
Comments on 2D Type IIA String and Matrix Model
We consider a type IIA-like string theory with RR-flux in two dimension and
propose its matrix model dual. This string theory describes a Majorana fermion
in the two dimensional spacetime. We also discuss its scattering amplitudes
both in the world-sheet theory and in the matrix model.Comment: 21 pages, Harvmac, to appear in JHEP, relation to 2d superstring
constructed by D. Kutasov hep-th/9110041 is clarifie
On Type II Strings in Two Dimensions
We consider type IIA/B strings in two-dimensions and their projection with
respect to the nilpotent space-time supercharge. Based on the ground ring
structure, we propose a duality between perturbed type II strings and the
topological B-model on deformed Calabi-Yau singularities. Depending on the type
II spectra, one has either the conifold or the suspended pinch point geometry.
Using the corresponding quiver gauge theory, obtained by D-branes wrapping in
the resolved suspended pinch point geometry, we propose the all orders
perturbative partition function.Comment: 1+23 page
Stringy Instantons and Quiver Gauge Theories
We explore contributions to the 4D effective superpotential which arise from
Euclidean D3 branes (``instantons'') that intersect space-filling D-branes.
These effects can perturb the effective field theory on the space-filling
branes by nontrivial operators composed of charged matter fields, changing the
vacuum structure in a qualitative way in some examples. Our considerations are
exemplified throughout by a careful study of a fractional brane configuration
on a del Pezzo surface.Comment: 30 pages, 4 figures; v2: reference added; v3: confusing minor error
in axion charges fixed (thanks to D. Green for pointing it out
Non-relativistic metrics from back-reacting fermions
It has recently been pointed out that under certain circumstances the
back-reaction of charged, massive Dirac fermions causes important modifications
to AdS_2 spacetimes arising as the near horizon geometry of extremal black
holes. In a WKB approximation, the modified geometry becomes a non-relativistic
Lifshitz spacetime. In three dimensions, it is known that integrating out
charged, massive fermions gives rise to gravitational and Maxwell Chern-Simons
terms. We show that Schrodinger (warped AdS_3) spacetimes exist as solutions to
a gravitational and Maxwell Chern-Simons theory with a cosmological constant.
Motivated by this, we look for warped AdS_3 or Schrodinger metrics as exact
solutions to a fully back-reacted theory containing Dirac fermions in three and
four dimensions. We work out the dynamical exponent in terms of the fermion
mass and generalize this result to arbitrary dimensions.Comment: 26 pages, v2: typos corrected, references added, minor change
Backlund Transformations, D-Branes, and Fluxes in Minimal Type 0 Strings
We study the Type 0A string theory in the (2,4k) superconformal minimal model
backgrounds, focusing on the fully non-perturbative string equations which
define the partition function of the model. The equations admit a parameter,
Gamma, which in the spacetime interpretation controls the number of background
D-branes, or R-R flux units, depending upon which weak coupling regime is
taken. We study the properties of the string equations (often focusing on the
(2,4) model in particular) and their physical solutions. The solutions are the
potential for an associated Schrodinger problem whose wavefunction is that of
an extended D-brane probe. We perform a numerical study of the spectrum of this
system for varying Gamma and establish that when Gamma is a positive integer
the equations' solutions have special properties consistent with the spacetime
interpretation. We also show that a natural solution-generating transformation
(that changes Gamma by an integer) is the Backlund transformation of the KdV
hierarchy specialized to (scale invariant) solitons at zero velocity. Our
results suggest that the localized D-branes of the minimal string theories are
directly related to the solitons of the KdV hierarchy. Further, we observe an
interesting transition when Gamma=-1.Comment: 17 pages, 3 figure
D-Branes and Fluxes in Supersymmetric Quantum Mechanics
Type 0A string theory in the (2,4k) superconformal minimal model backgrounds,
with background ZZ D-branes or R-R fluxes can be formulated non-perturbatively.
The branes and fluxes have a description as threshold bound states in an
associated one-dimensional quantum mechanics which has a supersymmetric
structure, familiar from studies of the generalized KdV system. The relevant
bound state wavefunctions in this problem have unusual asymptotics (they are
not normalizable in general, and break supersymmetry) which are consistent with
the underlying description in terms of open and closed string sectors. The
overall organization of the physics is very pleasing: The physics of the closed
strings in the background of branes or fluxes is captured by the generalized
KdV system and non-perturbative string equations obtained by reduction of that
system (the hierarchy of equations found by Dalley, Johnson, Morris and
Watterstam). Meanwhile, the bound states wavefunctions, which describe the
physics of the ZZ D-brane (or flux) background in interaction with probe FZZT
D-branes, are captured by the generalized mKdV system, and non-perturbative
string equations obtained by reduction of that system (the Painleve II hierachy
found by Periwal and Shevitz in this context).Comment: 41 pages, LaTe
A Matrix Big Bang
The light-like linear dilaton background represents a particularly simple
time-dependent 1/2 BPS solution of critical type IIA superstring theory in ten
dimensions. Its lift to M-theory, as well as its Einstein frame metric, are
singular in the sense that the geometry is geodesically incomplete and the
Riemann tensor diverges along a light-like subspace of codimension one. We
study this background as a model for a big bang type singularity in string
theory/M-theory. We construct the dual Matrix theory description in terms of a
(1+1)-d supersymmetric Yang-Mills theory on a time-dependent world-sheet given
by the Milne orbifold of (1+1)-d Minkowski space. Our model provides a
framework in which the physics of the singularity appears to be under control.Comment: 25 pages, LaTeX; v2: discussion of singularity of Einstein frame
metric added, references adde
Classification of All 1/2 BPS Solutions of the Tiny Graviton Matrix Theory
The tiny graviton matrix theory [hep-th/0406214] is proposed to describe DLCQ
of type IIB string theory on the maximally supersymmetric plane-wave or
AdS_5xS^5 background. In this paper we provide further evidence in support of
the tiny graviton conjecture by focusing on the zero energy, half BPS
configurations of this matrix theory and classify all of them. These vacua are
generically of the form of various three sphere giant gravitons. We clarify the
connection between our solutions and the half BPS configuration in N=4 SYM
theory and their gravity duals. Moreover, using our half BPS solutions, we show
how the tiny graviton Matrix theory and the mass deformed D=3, N=8
superconformal field theories are related to each other.Comment: 40 pages, 12 figures, v
BPS Operators in N=4 SYM: Calogero Models and 2D Fermions
A connection between the gauge fixed dynamics of protected operators in
superconformal Yang-Mills theory in four dimensions and Calogero systems is
established. This connection generalizes the free Fermion description of the
chiral primary operators of the gauge theory formed out of a single complex
scalar to more general operators. In particular, a detailed analysis of
protected operators charged under an su(1|1)contained in psu(2,2|4) is carried
out and a class of operators is identified, whose dynamics is described by the
rational super-Calogero model. These results are generalized to arbitrary BPS
operators charged under an su(2|3) of the superconformal algebra. Analysis of
the non-local symmetries of the super-Calogero model is also carried out, and
it is shown that symmetry for a large class of protected operators is a
contraction of the corresponding Yangian algebra to a loop algebra.Comment: 29 pages, 3 figure