52 research outputs found
World Volume Noncommutativity versus Target Space Noncommutativity
It is known that the noncommutativity of D-brane coordinate is responsible
for describing the higher-dimensional D-branes in terms of more fundamental
ones such as D-particles or D-instantons, while considering a noncommutative
torus as a target space is conjectured to be equivalent to introducing the
background antisymmetric tensor field in matrix models. In the present paper we
clarify the dual nature of both descriptions. Namely the noncommutativity of
conjugate momenta of the D-brane coordinates realizes the target space
structure, whereas noncommutativity of the coordinates themselves realizes
world volume structure. We explicitly construct a boundary state for the
Dirichlet boundary condition where the string boundary is adhered to the
D-brane on the noncommutative torus. There are non-trivial relations between
the parameters appeared in the algebra of the coordinates and that of the
momenta.Comment: 17 pages, LaTex, no figure
Existence of new nonlocal field theory on noncommutative space and spiral flow in renormalization group analysis of matrix models
In the previous study, we formulate a matrix model renormalization group
based on the fuzzy spherical harmonics with which a notion of high/low energy
can be attributed to matrix elements, and show that it exhibits locality and
various similarity to the usual Wilsonian renormalization group of quantum
field theory. In this work, we continue the renormalization group analysis of a
matrix model with emphasis on nonlocal interactions where the fields on
antipodal points are coupled. They are indeed generated in the renormalization
group procedure and are tightly related to the noncommutative nature of the
geometry. We aim at formulating renormalization group equations including such
nonlocal interactions and finding existence of nontrivial field theory with
antipodal interactions on the fuzzy sphere. We find several nontrivial fixed
points and calculate the scaling dimensions associated with them. We also
consider the noncommutative plane limit and then no consistent fixed point is
found. This contrast between the fuzzy sphere limit and the noncommutative
plane limit would be manifestation in our formalism of the claim given by Chu,
Madore and Steinacker that the former does not have UV/IR mixing, while the
latter does.Comment: 1+47 pages, no figure; Ver. 2, references and some comments are
added; Ver. 3, typos corrected. Version to appear in JHE
Supersymmetric double-well matrix model as two-dimensional type IIA superstring on RR background
In the previous paper, the authors pointed out correspondence of a
supersymmetric double-well matrix model with two-dimensional type IIA
superstring theory on a nontrivial Ramond-Ramond background from the viewpoint
of symmetries and spectrum. In this paper we further investigate the
correspondence from dynamical aspects by comparing scattering amplitudes in the
matrix model and those in the type IIA theory. In the latter, cocycle factors
are introduced to vertex operators in order to reproduce correct transformation
laws and target-space statistics. By a perturbative treatment of the
Ramond-Ramond background as insertions of the corresponding vertex operators,
various IIA amplitudes are explicitly computed including quantitatively precise
numerical factors. We show that several kinds of amplitudes in both sides
indeed have exactly the same dependence on parameters of the theory. Moreover,
we have a number of relations among coefficients which connect quantities in
the type IIA theory and those in the matrix model. Consistency of the relations
convinces us of the validity of the correspondence.Comment: 52 pages, version to appear in JHE
T-duality of ZZ-brane
We examine how nonperturbative effects in string theory are transformed under
the T-duality in its nonperturbative framework by analyzing the c=1/2
noncritical string theory as a simplest example. We show that in the T-dual
theory they also take the form of exp(-S_0/g_s) in the leading order and that
the instanton actions S_0 of the dual ZZ-branes are exactly the same as those
in the original c=1/2 string theory. Furthermore we present formulas for
coefficients of exp(-S_0/g_s) in the dual theory.Comment: 37 pages, no figure, LaTeX; (v2) version published in Physical Review
Resurgence of one-point functions in a matrix model for 2D type IIA superstrings
In the previous papers, the authors pointed out correspondence between a
supersymmetric double-well matrix model and two-dimensional type IIA
superstring theory on a Ramond-Ramond background. This was confirmed by
agreement between planar correlation functions in the matrix model and
tree-level amplitudes in the superstring theory. Furthermore, in the matrix
model we computed one-point functions of single-trace operators to all orders
of genus expansion in its double scaling limit, and found that the large-order
behavior of this expansion is stringy and not Borel summable. In this paper, we
discuss resurgence structure of these one-point functions and see cancellations
of ambiguities in their trans-series. More precisely, we compute both series of
ambiguities arising in a zero-instanton sector and in a one-instanton sector,
and confirm how they cancel each other. In case that the original integration
contour is a finite interval not passing through a saddle point, we have to
choose an appropriate integration path in order for resurgence to work.Comment: 25 pages, 2 figures, typos correcte
Manifestly T-Duality Symmetric Matrix Models
We present a new class of matrix models which are manifestly symmetric under
the T-duality transformation of the target space. The models may serve as a
nonperturbative regularization for the T-duality symmetry in continuum string
theory. In particular, it now becomes possible to extract winding modes
explicitly in terms of extended matrix variables.Comment: REVTeX, 15 pages, no figure
Noncommutativities of D-branes and -changing Degrees of Freedom in D-brane Matrix Models
It is known that when there are several D-branes, their space-time
coordinates in general become noncommutative. From the point of view of
noncommutative geometry, it reflects noncommutativity of the world volume of
the D-branes. On the other hand, as we showed in the previous work, in the
presence of the constant antisymmetric tensor field the momentum operators of
the D-branes have noncommutative structure. In the present paper, we
investigate a relation between these noncommutativities and the description of
D-branes in terms of the noncommutative Yang-Mills theory recently proposed by
Seiberg and Witten. It is shown that the noncommutativity of the Yang-Mills
theory, which implies that of the world volume coordinates, originates from
both noncommutativities of the transverse coordinates and momenta from the
viewpoint of the lower-dimensional D-branes. Moreover, we show that this
noncommutativity is transformed by coordinate transformations on the world
volume and thereby can be chosen in an arbitrary fixed value. We also make a
brief comment on a relation between this fact and a hidden symmetry of the IIB
matrix models.Comment: 15 pages, LaTeX, no figures, arguments on the action and symmetry are
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