192 research outputs found
The Block Spin Renormalization Group Approach and Two-Dimensional Quantum Gravity
A block spin renormalization group approach is proposed for the dynamical
triangulation formulation of two-dimensional quantum gravity. The idea is to
update link flips on the block lattice in response to link flips on the
original lattice. Just as the connectivity of the original lattice is meant to
be a lattice representation of the metric, the block links are determined in
such a way that the connectivity of the block lattice represents a block
metric. As an illustration, this approach is applied to the Ising model coupled
to two-dimensional quantum gravity. The correct critical coupling is
reproduced, but the critical exponent is obscured by unusually large finite
size effects.Comment: 10 page
Fivebranes from gauge theory
We study theories with sixteen supercharges and a discrete energy spectrum.
One class of theories has symmetry group . They arise as truncations
of super Yang Mills. They include the plane wave matrix model, 2+1
super Yang Mills on and super Yang Mills on . We explain how to obtain their gravity duals in a unified way.
We explore the regions of the geometry that are relevant for the study of some
1/2 BPS and near BPS states. This leads to a class of two dimensional (4,4)
supersymmetric sigma models with non-zero flux, including a massive
deformed WZW model. We show how to match some features of the string spectrum
with the Yang Mills theory.
The other class of theories are also connected to super Yang
Mills and arise by making some of the transverse scalars compact. Their vacua
are characterized by a 2d Yang Mills theory or 3d Chern Simons theory. These
theories realize peculiar superpoincare symmetry algebras in 2+1 or 1+1
dimensions with "non-central" charges. We finally discuss gravity duals of
super Yang Mills on .Comment: 50+24 pages, 9 figures, latex. v2: typos corrected, references adde
Robustness of equilibrium in the Kyle model of informed speculation
We analyze a static Kyle (1983) model in which a risk-neutral informed trader can use arbitrary (linear or non-linear) deterministic strategies, and a nite number of market makers can use arbitrary pricing rules. We establish a strong sense in which the linear Kyle equilibrium is robust: the rst variation in any agent's expected payo with respect to a small variation in his conjecture about the strategies of others vanishes at equilibrium. Thus, small errors in a market maker's beliefs about the informed speculator's trading strategy do not reduce his expected payo s. Therefore, the original equilibrium strategies remain optimal and still constitute an equilibrium (neglecting the higher-order terms.) We also establish that if a non-linear equilibrium exists, then it is not robust
A Matrix Model for AdS2
A matrix quantum mechanics with potential and an SL(2,R)
conformal symmetry is conjectured to be dual to two-dimensional type 0A string
theory on AdS with units of RR flux.Comment: 12 page
The 1/N expansion of colored tensor models
In this paper we perform the 1/N expansion of the colored three dimensional
Boulatov tensor model. As in matrix models, we obtain a systematic topological
expansion, with more and more complicated topologies suppressed by higher and
higher powers of N. We compute the first orders of the expansion and prove that
only graphs corresponding to three spheres S^3 contribute to the leading order
in the large N limit.Comment: typos corrected, references update
Unexpected Spin-Off from Quantum Gravity
We propose a novel way of investigating the universal properties of spin
systems by coupling them to an ensemble of causal dynamically triangulated
lattices, instead of studying them on a fixed regular or random lattice.
Somewhat surprisingly, graph-counting methods to extract high- or
low-temperature series expansions can be adapted to this case. For the
two-dimensional Ising model, we present evidence that this ameliorates the
singularity structure of thermodynamic functions in the complex plane, and
improves the convergence of the power series.Comment: 10 pages, 4 figures; final, slightly amended version, to appear in
Physica
Bubble divergences: sorting out topology from cell structure
We conclude our analysis of bubble divergences in the flat spinfoam model. In
[arXiv:1008.1476] we showed that the divergence degree of an arbitrary
two-complex Gamma can be evaluated exactly by means of twisted cohomology.
Here, we specialize this result to the case where Gamma is the two-skeleton of
the cell decomposition of a pseudomanifold, and sharpen it with a careful
analysis of the cellular and topological structures involved. Moreover, we
explain in detail how this approach reproduces all the previous powercounting
results for the Boulatov-Ooguri (colored) tensor models, and sheds light on
algebraic-topological aspects of Gurau's 1/N expansion.Comment: 19 page
The basis of the physical Hilbert space of lattice gauge theories
Non-linear Fourier analysis on compact groups is used to construct an
orthonormal basis of the physical (gauge invariant) Hilbert space of
Hamiltonian lattice gauge theories. In particular, the matrix elements of the
Hamiltonian operator involved are explicitly computed. Finally, some
applications and possible developments of the formalism are discussed.Comment: 14 pages, LaTeX (Using amsmath
The complete 1/N expansion of colored tensor models in arbitrary dimension
In this paper we generalize the results of [1,2] and derive the full 1/N
expansion of colored tensor models in arbitrary dimensions. We detail the
expansion for the independent identically distributed model and the topological
Boulatov Ooguri model
2D Conformal Field Theories and Holography
It is known that the chiral part of any 2d conformal field theory defines a
3d topological quantum field theory: quantum states of this TQFT are the CFT
conformal blocks. The main aim of this paper is to show that a similar CFT/TQFT
relation exists also for the full CFT. The 3d topological theory that arises is
a certain ``square'' of the chiral TQFT. Such topological theories were studied
by Turaev and Viro; they are related to 3d gravity. We establish an
operator/state correspondence in which operators in the chiral TQFT correspond
to states in the Turaev-Viro theory. We use this correspondence to interpret
CFT correlation functions as particular quantum states of the Turaev-Viro
theory. We compute the components of these states in the basis in the
Turaev-Viro Hilbert space given by colored 3-valent graphs. The formula we
obtain is a generalization of the Verlinde formula. The later is obtained from
our expression for a zero colored graph. Our results give an interesting
``holographic'' perspective on conformal field theories in 2 dimensions.Comment: 29+1 pages, many figure
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