265,878 research outputs found

### Three dimensional massive scalar field theory and the derivative expansion of the renormalization group

We show that non-perturbative fixed points of the exact renormalization
group, their perturbations and corresponding massive field theories can all be
determined directly in the continuum -- without using bare actions or any
tuning procedure. As an example, we estimate the universal couplings of the
non-perturbative three-dimensional one-component massive scalar field theory in
the Ising model universality class, by using a derivative expansion (and no
other approximation). These are compared to the recent results from other
methods. At order derivative-squared approximation, the four-point coupling at
zero momentum is better determined by other methods, but factoring this out
appropriately, all our other results are in very close agreement with the most
powerful of these methods. In addition we provide for the first time, estimates
of the n-point couplings at zero momentum, with n=12,14, and the order
momentum-squared parts with n=2 ... 10.Comment: 33 pages, 1 eps figure, 7 tables; TeX + harvmac; version to appear in
Nucl. Phys.

### Large N and the renormalization group

In the large N limit, we show that the Local Potential Approximation to the
flow equation for the Legendre effective action, is in effect no longer an
approximation, but exact - in a sense, and under conditions, that we determine
precisely. We explain why the same is not true for the Polchinski or Wilson
flow equations and, by deriving an exact relation between the Polchinski and
Legendre effective potentials (that holds for all N), we find the correct large
N limit of these flow equations. We also show that all forms (and all parts) of
the renormalization group are exactly soluble in the large N limit, choosing as
an example, D dimensional O(N) invariant N-component scalar field theory.Comment: 13 pages, uses harvmac; Added: one page with further clarification of
the main results, discussion of earlier work, and new references. To be
published in Phys. Lett.

### Destabilization of Neutron Stars by Type I Dimension Bubbles

An inhomogeneous compactification of a higher dimensional spacetime can
result in the formation of type I dimension bubbles, i.e., nontopological
solitons which tend to absorb and entrap massive particle modes. We consider
possible consequences of a neutron star that harbors such a soliton. The
astrophysical outcome depends upon the model parameters for the dimension
bubble, with a special sensitivity to the bubble's energy scale. For relatively
small energy scales, the bubble tends to rapidly consume the star without
forming a black hole. For larger energy scales, the bubble grows to a critical
mass, then forms a black hole within the star, which subsequently causes the
remaining star to collapse. It is possible that the latter scenario is
associated with core collapse explosions and gamma ray bursts.Comment: 8 pages; to appear in Phys.Lett.

### On the Fixed-Point Structure of Scalar Fields

In a recent Letter (K.Halpern and K.Huang, Phys. Rev. Lett. 74 (1995) 3526),
certain properties of the Local Potential Approximation (LPA) to the Wilson
renormalization group were uncovered, which led the authors to conclude that
$D>2$ dimensional scalar field theories endowed with {\sl non-polynomial}
interactions allow for a continuum of renormalization group fixed points, and
that around the Gaussian fixed point, asymptotically free interactions exist.
If true, this could herald very important new physics, particularly for the
Higgs sector of the Standard Model. Continuing work in support of these ideas,
has motivated us to point out that we previously studied the same properties
and showed that they lead to very different conclusions. Indeed, in as much as
the statements in hep-th/9406199 are correct, they point to some deep and
beautiful facts about the LPA and its generalisations, but however no new
physics.Comment: Typos corrected. A Comment - to be published in Phys. Rev. Lett. 1
page, 1 eps figure, uses LaTeX, RevTex and eps

### Derivative expansion of the renormalization group in O(N) scalar field theory

We apply a derivative expansion to the Legendre effective action flow
equations of O(N) symmetric scalar field theory, making no other approximation.
We calculate the critical exponents eta, nu, and omega at the both the leading
and second order of the expansion, associated to the three dimensional
Wilson-Fisher fixed points, at various values of N. In addition, we show how
the derivative expansion reproduces exactly known results, at special values
N=infinity,-2,-4, ... .Comment: 29 pages including 4 eps figures, uses LaTeX, epsfig, and latexsy

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