112 research outputs found
Holographic Renormalization Group Structure in Higher-Derivative Gravity
Classical higher-derivative gravity is investigated in the context of the
holographic renormalization group (RG). We parametrize the Euclidean time such
that one step of time evolution in (d+1)-dimensional bulk gravity can be
directly interpreted as that of block spin transformation of the d-dimensional
boundary field theory. This parametrization simplifies the analysis of the
holographic RG structure in gravity systems, and conformal fixed points are
always described by AdS geometry. We find that higher-derivative gravity
generically induces extra degrees of freedom which acquire huge mass around
stable fixed points and thus are coupled to highly irrelevant operators at the
boundary. In the particular case of pure R^2-gravity, we show that some region
of the coefficients of curvature-squared terms allows us to have two fixed
points (one is multicritical) which are connected by a kink solution. We
further extend our analysis to Minkowski time to investigate a model of
expanding universe described by the action with curvature-squared terms and
positive cosmological constant, and show that, in any dimensionality but four,
one can have a classical solution which describes time evolution from a de
Sitter geometry to another de Sitter geometry, along which the Hubble parameter
changes drastically.Comment: 26 pages, 6 figures, typos correcte
Gradient flow and the renormalization group
We investigate the renormalization group (RG) structure of the gradient flow.
Instead of using the original bare action to generate the flow, we propose to
use the effective action at each flow time. We write down the basic equation
for scalar field theory that determines the evolution of the action, and argue
that the equation can be regarded as a RG equation if one makes a
field-variable transformation at every step such that the kinetic term is kept
to take the canonical form. We consider a local potential approximation (LPA)
to our equation, and show that the result has a natural interpretation with
Feynman diagrams. We make an expansion of the LPA and show that
it reproduces the eigenvalues of the linearized RG transformation around both
the Gaussian and the Wilson-Fisher fixed points to the order of .Comment: 11 pages, 1 figure; v2, v3: typos corrected, some discussions
improve
Comments on D-Instantons in c<1 Strings
We suggest that the boundary cosmological constant \zeta in c<1 unitary
string theory be regarded as the one-dimensional complex coordinate of the
target space on which the boundaries of world-sheets can live. From this
viewpoint we explicitly construct analogues of D-instantons which satisfy
Polchinski's ``combinatorics of boundaries.'' We further show that our operator
formalism developed in the preceding articles is powerful in evaluating
D-instanton effects, and also demonstrate for simple cases that these effects
exactly coincide with the stringy nonperturbative effects found in the exact
solutions of string equations.Comment: 12 pages with 1 figure, LaTex, Version to appear in PL
A Note on the Weyl Anomaly in the Holographic Renormalization Group
We give a prescription for calculating the holographic Weyl anomaly in
arbitrary dimension within the framework based on the Hamilton-Jacobi equation
proposed by de Boer, Verlinde and Verlinde. A few sample calculations are made
and shown to reproduce the results that are obtained to this time with a
different method. We further discuss continuum limits, and argue that the
holographic renormalization group may describe the renormalized trajectory in
the parameter space. We also clarify the relationship of the present formalism
to the analysis carried out by Henningson and Skenderis.Comment: LaTeX, 24 pages, 2 figures, typos correcte
Master equation for the Unruh-DeWitt detector and the universal relaxation time in de Sitter space
We derive the master equation that completely determines the time evolution
of the density matrix of the Unruh-DeWitt detector in an arbitrary background
geometry. We apply the equation to reveal a nonequilibrium thermodynamic
character of de Sitter space. This generalizes an earlier study on the
thermodynamic property of the Bunch-Davies vacuum that an Unruh-DeWitt detector
staying in the Poincare patch and interacting with a scalar field in the
Bunch-Davies vacuum behaves as if it is in a thermal bath of finite
temperature. In this paper, instead of the Bunch-Davies vacuum, we consider a
class of initial states of scalar field, for which the detector behaves as if
it is in a medium that is not in thermodynamic equilibrium and that undergoes a
relaxation to the equilibrium corresponding to the Bunch-Davies vacuum. We give
a prescription for calculating the relaxation times of the nonequilibrium
processes. We particularly show that, when the initial state of the scalar
field is the instantaneous ground state at a finite past, the relaxation time
is always given by a universal value of half the curvature radius of de Sitter
space. We expect that the relaxation time gives a nonequilibrium thermodynamic
quantity intrinsic to de Sitter space.Comment: 41 pages, 10 figures; v2: typos corrected; v3: typos corrected; v4:
clarifications and references added; v5: final version appearing in PR
Noncommutative inflation and the large-scale damping in the CMB anisotropy
We show that a certain class of short-distance cutoff can give rise to large
suppression on the CMB anisotropies at large angular scales.Comment: 7 pages, 2 figures. Fonts changed. Talk given at QTS3 (Cincinnati,
OH, Sept. 2003
Holographic Renormalization Group
The holographic renormalization group (RG) is reviewed in a self-contained
manner. The holographic RG is based on the idea that the radial coordinate of a
space-time with asymptotically AdS geometry can be identified with the RG flow
parameter of the boundary field theory. After briefly discussing basic aspects
of the AdS/CFT correspondence, we explain how the notion of the holographic RG
comes out in the AdS/CFT correspondence. We formulate the holographic RG based
on the Hamilton-Jacobi equations for bulk systems of gravity and scalar fields,
as was introduced by de Boer, Verlinde and Verlinde. We then show that the
equations can be solved with a derivative expansion by carefully extracting
local counterterms from the generating functional of the boundary field theory.
The calculational methods to obtain the Weyl anomaly and scaling dimensions are
presented and applied to the RG flow from the N=4 SYM to an N=1 superconformal
fixed point discovered by Leigh and Strassler. We further discuss a relation
between the holographic RG and the noncritical string theory, and show that the
structure of the holographic RG should persist beyond the supergravity
approximation as a consequence of the renormalizability of the nonlinear sigma
model action of noncritical strings. As a check, we investigate the holographic
RG structure of higher-derivative gravity systems, and show that such systems
can also be analyzed based on the Hamilton-Jacobi equations, and that the
behaviour of bulk fields are determined solely by their boundary values. We
also point out that higher-derivative gravity systems give rise to new
multicritical points in the parameter space of the boundary field theories.Comment: 95 pages, 6 figures. Typos are corrected. References and a discussion
about continuum limit are adde
Comments on T-dualities of Ramond-Ramond Potentials
The type IIA/IIB effective actions compactified on T^d are known to be
invariant under the T-duality group SO(d, d; Z) although the invariance of the
R-R sector is not so direct to see. Inspired by a work of Brace, Morariu and
Zumino,we introduce new potentials which are mixture of R-R potentials and the
NS-NS 2-form in order to make the invariant structure of R-R sector more
transparent. We give a simple proof that if these new potentials transform as a
Majorana-Weyl spinor of SO(d, d; Z), the effective actions are indeed invariant
under the T-duality group. The argument is made in such a way that it can apply
to Kaluza-Klein forms of arbitrary degree. We also demonstrate that these new
fields simplify all the expressions including the Chern-Simons term.Comment: 26 pages; LaTeX; major version up; discussion on the Chern-Simons
term added; references adde
Matter fields in triangle-hinge models
The worldvolume theory of membrane is mathematically equivalent to
three-dimensional quantum gravity coupled to matter fields corresponding to the
target space coordinates of embedded membrane. In a recent paper
[arXiv:1503.08812] a new class of models are introduced that generate
three-dimensional random volumes, where the Boltzmann weight of each
configuration is given by the product of values assigned to the triangles and
the hinges. These triangle-hinge models describe three-dimensional pure gravity
and are characterized by semisimple associative algebras. In this paper, we
introduce matter degrees of freedom to the models by coloring simplices in a
way that they have local interactions. This is achieved simply by extending the
associative algebras of the original triangle-hinge models, and the profile of
matter field is specified by the set of colors and the form of interactions.
The dynamics of a membrane in -dimensional spacetime can then be described
by taking the set of colors to be . By taking another set of
colors, we can also realize three-dimensional quantum gravity coupled to the
Ising model, the -state Potts models or the RSOS models. One can actually
assign colors to simplices of any dimensions (tetrahedra, triangles, edges and
vertices), and three-dimensional colored tensor models can be realized as
triangle-hinge models by coloring tetrahedra, triangles and edges at a time.Comment: 21 pages, 14 figures. v2: discussions in section 4 improved. v3:
title changed, introduction enlarge
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