2,909 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
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
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
Continuous distributions of D3-branes and gauged supergravity
States on the Coulomb branch of N=4 super-Yang-Mills theory are studied from
the point of view of gauged supergravity in five dimensions. These
supersymmetric solutions provide examples of consistent truncation from type
IIB supergravity in ten dimensions. A mass gap for states created by local
operators and perfect screening for external quarks arise in the supergravity
approximation. We offer an interpretation of these surprising features in terms
of ensembles of brane distributions.Comment: 19 pages, two figures, latex. v2: reference added, small corrections.
v3: corrected unbounded spectrum erro
The Hidden Spatial Geometry of Non-Abelian Gauge Theories
The Gauss law constraint in the Hamiltonian form of the gauge theory
of gluons is satisfied by any functional of the gauge invariant tensor variable
. Arguments are given that the tensor is a more appropriate variable. When the Hamiltonian
is expressed in terms of or , the quantity appears.
The gauge field Bianchi and Ricci identities yield a set of partial
differential equations for in terms of . One can show that
is a metric-compatible connection for with torsion, and that the curvature
tensor of is that of an Einstein space. A curious 3-dimensional
spatial geometry thus underlies the gauge-invariant configuration space of the
theory, although the Hamiltonian is not invariant under spatial coordinate
transformations. Spatial derivative terms in the energy density are singular
when . These singularities are the analogue of the centrifugal
barrier of quantum mechanics, and physical wave-functionals are forced to
vanish in a certain manner near . It is argued that such barriers are
an inevitable result of the projection on the gauge-invariant subspace of the
Hilbert space, and that the barriers are a conspicuous way in which non-abelian
gauge theories differ from scalar field theories.Comment: 19 pages, TeX, CTP #223
Renormalization Group Flows from Holography--Supersymmetry and a c-Theorem
We obtain first order equations that determine a supersymmetric kink solution
in five-dimensional N=8 gauged supergravity. The kink interpolates between an
exterior anti-de Sitter region with maximal supersymmetry and an interior
anti-de Sitter region with one quarter of the maximal supersymmetry. One eighth
of supersymmetry is preserved by the kink as a whole. We interpret it as
describing the renormalization group flow in N=4 super-Yang-Mills theory broken
to an N=1 theory by the addition of a mass term for one of the three adjoint
chiral superfields. A detailed correspondence is obtained between fields of
bulk supergravity in the interior anti-de Sitter region and composite operators
of the infrared field theory. We also point out that the truncation used to
find the reduced symmetry critical point can be extended to obtain a new N=4
gauged supergravity theory holographically dual to a sector of N=2 gauge
theories based on quiver diagrams.
We consider more general kink geometries and construct a c-function that is
positive and monotonic if a weak energy condition holds in the bulk gravity
theory. For even-dimensional boundaries, the c-function coincides with the
trace anomaly coefficients of the holographically related field theory in
limits where conformal invariance is recovered.Comment: 56 pages, three figures, harvmac. v2: improved referencing, corrected
discussion of energy conditions. v3: one more reference fixe
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