17,035 research outputs found
Differential Regularization of a Non-relativistic Anyon Model
Differential regularization is applied to a field theory of a
non-relativistic charged boson field with
self-interaction and coupling to a statistics-changing Chern-Simons
gauge field. Renormalized configuration-space amplitudes for all diagrams
contributing to the 4-point function, which
is the only primitively divergent Green's function, are obtained up to 3-loop
order. The renormalization group equations are explicitly checked, and the
scheme dependence of the -function is investigated. If the
renormalization scheme is fixed to agree with a previous 1-loop calculation,
the 2- and 3-loop contributions to vanish, and
itself vanishes when the ``self-dual'' condition relating
to the gauge coupling is imposed.Comment: 22 pages in ReVTEX (with a plaintext PostScript figure appended at
end), MIT CTP #221
Nonperturbative Formulas for Central Functions of Supersymmetric Gauge Theories
For quantum field theories that flow between ultraviolet and infrared fixed
points, central functions, defined from two-point correlators of the stress
tensor and conserved currents, interpolate between central charges of the UV
and IR critical theories. We develop techniques that allow one to calculate the
flows of the central charges and that of the Euler trace anomaly coefficient in
a general N=1 supersymmetric gauge theory. Exact, explicit formulas for
gauge theories in the conformal window are given and analysed. The
Euler anomaly coefficient always satisfies the inequality .
This is new evidence in strongly coupled theories that this quantity satisfies
a four-dimensional analogue of the -theorem, supporting the idea of
irreversibility of the RG flow. Various other implications are discussed.Comment: latex, 27 page
Extremal Correlators in the AdS/CFT Correspondence
The non-renormalization of the 3-point functions of chiral primary operators in N=4 super-Yang-Mills theory is one of
the most striking facts to emerge from the AdS/CFT correspondence. A two-fold
puzzle appears in the extremal case, e.g. k_1 = k_2 + k_3. First, the
supergravity calculation involves analytic continuation in the k_i variables to
define the product of a vanishing bulk coupling and an infinite integral over
AdS. Second, extremal correlators are uniquely sensitive to mixing of the
single-trace operators with protected multi-trace operators in the
same representation of SU(4). We show that the calculation of extremal
correlators from supergravity is subject to the same subtlety of regularization
known for the 2-point functions, and we present a careful method which
justifies the analytic continuation and shows that supergravity fields couple
to single traces without admixture. We also study extremal n-point functions of
chiral primary operators, and argue that Type IIB supergravity requires that
their space-time form is a product of n-1 two-point functions (as in the free
field approximation) multiplied by a non-renormalized coefficient. This
non-renormalization property of extremal n-point functions is a new prediction
of the AdS/CFT correspondence. As a byproduct of this work we obtain the cubic
couplings and of fields in the dilaton and 5-sphere
graviton towers of Type IIB supergravity on .Comment: 26 pages, LateX, no figure
Comments on 4-point functions in the CFT/AdS correspondence
We study the four--point function of chiral primaries corresponding to the
dilaton--axion sector in supergravity in the /CFT correspondence. We
find relations between some of the supergravity graphs and compute their
leading singularities. We discuss the issue of logarithmic singularities and
their significance for the OPE structure of the CFT.Comment: Latex, 12 pages, Some typos correcte
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