185 research outputs found
Large N reduction for Chern-Simons theory on S^3
We study a matrix model which is obtained by dimensional reduction of
Chern-Simon theory on S^3 to zero dimension. We find that expanded around a
particular background consisting of multiple fuzzy spheres, it reproduces the
original theory on S^3 in the planar limit. This is viewed as a new type of the
large N reduction generalized to curved space.Comment: 4 pages, 2 figures, references added, typos correcte
Coarse-Graining the Lin-Maldacena Geometries
The Lin-Maldacena geometries are nonsingular gravity duals to degenerate
vacuum states of a family of field theories with SU(2|4) supersymmetry. In this
note, we show that at large N, where the number of vacuum states is large,
there is a natural `macroscopic' description of typical states, giving rise to
a set of coarse-grained geometries. For a given coarse-grained state, we can
associate an entropy related to the number of underlying microstates. We find a
simple formula for this entropy in terms of the data that specify the geometry.
We see that this entropy function is zero for the original microstate
geometries and maximized for a certain ``typical state'' geometry, which we
argue is the gravity dual to the zero-temperature limit of the thermal state of
the corresponding field theory. Finally, we note that the coarse-grained
geometries are singular if and only if the entropy function is non-zero.Comment: 29 pages, LaTeX, 3 figures; v2 references adde
Bounces/Dyons in the Plane Wave Matrix Model and SU(N) Yang-Mills Theory
We consider SU(N) Yang-Mills theory on the space R^1\times S^3 with Minkowski
signature (-+++). The condition of SO(4)-invariance imposed on gauge fields
yields a bosonic matrix model which is a consistent truncation of the plane
wave matrix model. For matrices parametrized by a scalar \phi, the Yang-Mills
equations are reduced to the equation of a particle moving in the double-well
potential. The classical solution is a bounce, i.e. a particle which begins at
the saddle point \phi=0 of the potential, bounces off the potential wall and
returns to \phi=0. The gauge field tensor components parametrized by \phi are
smooth and for finite time both electric and magnetic fields are nonvanishing.
The energy density of this non-Abelian dyon configuration does not depend on
coordinates of R^1\times S^3 and the total energy is proportional to the
inverse radius of S^3. We also describe similar bounce dyon solutions in SU(N)
Yang-Mills theory on the space R^1\times S^2 with signature (-++). Their energy
is proportional to the square of the inverse radius of S^2. From the viewpoint
of Yang-Mills theory on R^{1,1}\times S^2 these solutions describe non-Abelian
(dyonic) flux tubes extended along the x^3-axis.Comment: 11 pages; v2: one formula added, some coefficients correcte
Absence of sign problem in two-dimensional N=(2,2) super Yang-Mills on lattice
We show that N=(2,2) SU(N) super Yang-Mills theory on lattice does not have
sign problem in the continuum limit, that is, under the phase-quenched
simulation phase of the determinant localizes to 1 and hence the phase-quench
approximation becomes exact. Among several formulations, we study models by
Cohen-Kaplan-Katz-Unsal (CKKU) and by Sugino. We confirm that the sign problem
is absent in both models and that they converge to the identical continuum
limit without fine tuning. We provide a simple explanation why previous works
by other authors, which claim an existence of the sign problem, do not capture
the continuum physics.Comment: 27 pages, 24 figures; v2: comments and references added; v3: figures
on U(1) mass independence and references added, to appear in JHE
Formulation of Supersymmetry on a Lattice as a Representation of a Deformed Superalgebra
The lattice superalgebra of the link approach is shown to satisfy a Hopf
algebraic supersymmetry where the difference operator is introduced as a
momentum operator. The breakdown of the Leibniz rule for the lattice difference
operator is accommodated as a coproduct operation of (quasi)triangular Hopf
algebra and the associated field theory is consistently defined as a braided
quantum field theory. Algebraic formulation of path integral is perturbatively
defined and Ward-Takahashi identity can be derived on the lattice. The claimed
inconsistency of the link approach leading to the ordering ambiguity for a
product of fields is solved by introducing an almost trivial braiding structure
corresponding to the triangular structure of the Hopf algebraic superalgebra.
This could be seen as a generalization of spin and statistics relation on the
lattice. From the consistency of this braiding structure of fields a grading
nature for the momentum operator is required.Comment: 45 page
Boundary operators in minimal Liouville gravity and matrix models
We interpret the matrix boundaries of the one matrix model (1MM) recently
constructed by two of the authors as an outcome of a relation among FZZT
branes. In the double scaling limit, the 1MM is described by the (2,2p+1)
minimal Liouville gravity. These matrix operators are shown to create a
boundary with matter boundary conditions given by the Cardy states. We also
demonstrate a recursion relation among the matrix disc correlator with two
different boundaries. This construction is then extended to the two matrix
model and the disc correlator with two boundaries is compared with the
Liouville boundary two point functions. In addition, the realization within the
matrix model of several symmetries among FZZT branes is discussed.Comment: 26 page
Lattice formulation of two-dimensional N=(2,2) super Yang-Mills with SU(N) gauge group
We propose a lattice model for two-dimensional SU(N) N=(2,2) super Yang-Mills
model. We start from the CKKU model for this system, which is valid only for
U(N) gauge group. We give a reduction of U(1) part keeping a part of
supersymmetry. In order to suppress artifact vacua, we use an admissibility
condition.Comment: 16 pages, 3 figures; v2: typo crrected; v3: 18 pages, a version to
appear in JHE
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
Model of M-theory with Eleven Matrices
We show that an action of a supermembrane in an eleven-dimensional spacetime
with a semi-light-cone gauge can be written only with Nambu-Poisson bracket and
an invariant symmetric bilinear form under an approximation. Thus, the action
under the conditions is manifestly covariant under volume preserving
diffeomorphism even when the world-volume metric is flat. Next, we propose two
3-algebraic models of M-theory which are obtained as a second quantization of
an action that is equivalent to the supermembrane action under the
approximation. The second quantization is defined by replacing Nambu-Poisson
bracket with finite-dimensional 3-algebras' brackets. Our models include eleven
matrices corresponding to all the eleven space-time coordinates in M-theory
although they possess not SO(1,10) but SO(1,2) x SO(8) or SO(1,2) x SU(4) x
U(1) covariance. They possess N=1 space-time supersymmetry in eleven dimensions
that consists of 16 kinematical and 16 dynamical ones. We also show that the
SU(4) model with a certain algebra reduces to BFSS matrix theory if DLCQ limit
is taken.Comment: 20 pages, references, a table and discussions added, typos correcte
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
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