22 research outputs found
Bubbling 1/2 BPS Geometries and Penrose Limits
We discuss how to take a Penrose limit in bubbling 1/2 BPS geometries at the
stage of a single function z(x_1,x_2,y). By starting from the z of the AdS_5 x
S^5 we can directly derive that of the pp-wave via the Penrose limit. In that
time the function z for the pp-wave with 1/R^2-corrections is obtained. We see
that it surely reproduces the pp-wave with 1/R^2 terms. In addition we consider
the Penrose limit in the configuration of the concentric rings.Comment: 15 pages, 3 figures, LaTeX, v2:higher order corrections are added,
typos corrected and references added, version to appear in PR
Open Semiclassical Strings and Long Defect Operators in AdS/dCFT Correspondence
We consider defect composite operators in a defect superconformal field
theory obtained by inserting an AdS_4 x S^2-brane in the AdS_5 x S^5
background. The one-loop dilatation operator for the scalar sector is
represented by an integrable open spin chain. We give a description to
construct coherent states for the open spin chain. Then, by evaluating the
expectation value of the Hamiltonian with the coherent states in a long
operator limit, a Landau-Lifshitz type of sigma model action is obtained. This
action is also derived from the string action and hence we find a complete
agreement in both SYM and string sides. We see that an SO(3)_H pulsating string
solution is included in the action and its energy completely agrees with the
result calculated in a different method. In addition, we argue that our
procedure would be applicable to other AdS-brane cases.Comment: 22 pages, 1 figure, LaTeX, minor corrections and references added.
v3) some new results added. shortened and accepted version in PR
Effective Actions of Matrix Models on Homogeneous Spaces
We evaluate the effective actions of supersymmetric matrix models on fuzzy
S^2\times S^2 up to the two loop level. Remarkably it turns out to be a
consistent solution of IIB matrix model. Based on the power counting and SUSY
cancellation arguments, we can identify the 't Hooft coupling and large N
scaling behavior of the effective actions to all orders. In the large N limit,
the quantum corrections survive except in 2 dimensional limits. They are O(N)
and O(N^{4\over 3}) for 4 and 6 dimensional spaces respectively. We argue that
quantum effects single out 4 dimensionality among fuzzy homogeneous spaces.Comment: 28 pages, 1 figure, published version in Nucl. Phys.
Quantum Corrections on Fuzzy Sphere
We investigate quantum corrections in non-commutative gauge theory on fuzzy
sphere. We study translation invariant models which classically favor a single
fuzzy sphere with U(1) gauge group. We evaluate the effective actions up to the
two loop level. We find non-vanishing quantum corrections at each order even in
supersymmetric models. In particular the two loop contribution favors U(n)
gauge group over U(1) contrary to the tree action in a deformed IIB matrix
model with a Myers term. We further observe close correspondences to 2
dimensional quantum gravity.Comment: 27 pages, 1 figure, published version in Nucl Phys.
Embedding of theories with SU(2|4) symmetry into the plane wave matrix model
We study theories with SU(2|4) symmetry, which include the plane wave matrix
model, 2+1 SYM on RxS^2 and N=4 SYM on RxS^3/Z_k. All these theories possess
many vacua. From Lin-Maldacena's method which gives the gravity dual of each
vacuum, it is predicted that the theory around each vacuum of 2+1 SYM on RxS^2
and N=4 SYM on RxS^3/Z_k is embedded in the plane wave matrix model. We show
this directly on the gauge theory side. We clearly reveal relationships among
the spherical harmonics on S^3, the monopole harmonics and the harmonics on
fuzzy spheres. We extend the compactification (the T-duality) in matrix models
a la Taylor to that on spheres.Comment: 56 pages, 6 figures, v2:a footnote and references added, section 5.2
improved, typos corrected, v3:typos corrected, v4: some equations are
corrected, eq.(G.2) is added, conclusion is unchange
N=4 SYM on R x S^3 and Theories with 16 Supercharges
We study N=4 SYM on R x S^3 and theories with 16 supercharges arising as its
consistent truncations. These theories include the plane wave matrix model, N=4
SYM on R x S^2 and N=4 SYM on R x S^3/Z_k, and their gravity duals were studied
by Lin and Maldacena. We make a harmonic expansion of the original N=4 SYM on R
x S^3 and obtain each of the truncated theories by keeping a part of the
Kaluza-Klein modes. This enables us to analyze all the theories in a unified
way. We explicitly construct some nontrivial vacua of N=4 SYM on R x S^2. We
perform 1-loop analysis of the original and truncated theories. In particular,
we examine states regarded as the integrable SO(6) spin chain and a
time-dependent BPS solution, which is considered to correspond to the AdS giant
graviton in the original theory.Comment: 68 pages, 12 figures, v2,v3:typos corrected and comments added. To
appear in JHE
Complex Matrix Model and Fermion Phase Space for Bubbling AdS Geometries
We study a relation between droplet configurations in the bubbling AdS
geometries and a complex matrix model that describes the dynamics of a class of
chiral primary operators in dual N=4 super Yang Mills (SYM). We show rigorously
that a singlet holomorphic sector of the complex matrix model is equivalent to
a holomorphic part of two-dimensional free fermions, and establish an exact
correspondence between the singlet holomorphic sector of the complex matrix
model and one-dimensional free fermions. Based on this correspondence, we find
a relation of the singlet holomorphic operators of the complex matrix model to
the Wigner phase space distribution. By using this relation and the AdS/CFT
duality, we give a further evidence that the droplets in the bubbling AdS
geometries are identified with those in the phase space of the one-dimensional
fermions. We also show that the above correspondence actually maps the
operators of N=4 SYM corresponding to the (dual) giant gravitons to the droplet
configurations proposed in the literature.Comment: 27 pages, 6 figures, some clarification, typos corrected, published
versio
Stability of fuzzy geometry in IIB matrix model
We continue our study of the IIB matrix model on fuzzy .
Especially in this paper we focus on the case where the size of one of
is different from the other. By the power counting and SUSY
cancellation arguments, we can identify the 't Hooft coupling and large
scaling behavior of the effective action to all orders. We conclude that the
most symmetric configuration where the both s are of the
same size is favored at the two loop level. In addition we develop a new
approach to evaluate the amplitudes on fuzzy .Comment: 16 pages, 5 figures, latex, published version in Nucl. Phys.
Integrability and Higher Loops in AdS/dCFT Correspondence
We further study the correspondence between open semiclassical strings and
long defect operators which is discussed in our previous work [hep-th/0410139].
We give an interpretation of the spontaneous symmetry breaking of SO(6)->
SO(3)_H x SO(3)_V from the viewpoint of the Riemann surface by following the
argument of Minahan. Then we use the concrete form of the resolvent for a
single cut solution and compute the anomalous dimension of operators dual to an
open pulsating string at three-loop level. In the string side we obtain the
energy of the open pulsating string solution by semiclassical analysis. Both
results agree at two-loop level but we find a three-loop discrepancy.Comment: v1: 11 pages, 2 figures; v2: minor corrections, references added,
published versio
Open Spinning Strings and AdS/dCFT Duality
We consider open spinning string solutions on an AdS_4 x S^2-brane (D5-brane)
in the bulk AdS_5 x S^5 background. By taking account of the breaking of
SO(6)_R to SO(3)_H x SO(3)_V due to the presence of the AdS-brane, the open
rotating string ansatz is discussed. We construct the elliptic folded/circular
open string solutions in the SU(2) and the SL(2) sectors, so that they satisfy
the appropriate boundary conditions. On the other hand, in the SU(2) sector of
the gauge theory, we compute the matrix of anomalous dimension of the defect
operator, which turns out to be the Hamiltonian of an open integrable spin
chain. Then we consider the coordinate Bethe ansatz with arbitrary number of
impurities, and compare the boundary condition of the Bethe wavefunction with
that of the corresponding open string solution. We also discuss the Bethe
ansatz for the open SL(2) spin chain with several supports from the string
theory side. Then, in both SU(2) and SL(2) sectors, we analyze the Bethe
equations in the thermodynamic limit and formulate the `doubling trick' on the
Riemann surface associated with the gauge theory.Comment: 1+50 pages, 7 figures, JHEP style, references adde