157 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
Lattice Formulation for 2d N=(2,2), (4,4) Super Yang-Mills Theories without Admissibility Conditions
We present a lattice formulation for two-dimensional N=(2,2) and (4,4)
supersymmetric Yang-Mills theories that resolves vacuum degeneracy for gauge
fields without imposing admissibility conditions. Cases of U(N) and SU(N) gauge
groups are considered, gauge fields are expressed by unitary link variables,
and one or two supercharges are preserved on the two-dimensional square
lattice. There does not appear fermion doubler, and no fine-tuning is required
to obtain the desired continuum theories in a perturbative argument. This
formulation is expected to serve as a more convenient basis for numerical
simulations. The same approach will also be useful to other two-dimensional
supersymmetric lattice gauge theories with unitary link variables constructed
so far -- for example, N=(8,8) supersymmetric Yang-Mills theory and N=(2,2)
supersymmetric QCD.Comment: 19 pages, no figure, (v2) reference added, minor corrections, version
to be published in JHE
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
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
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