52 research outputs found
Integral Transforms for Conformal Field Theories with a Boundary
A new method is developed for solving the conformally invariant integrals
that arise in conformal field theories with a boundary. The presence of a
boundary makes previous techniques for theories without a boundary less
suitable. The method makes essential use of an invertible integral transform,
related to the radon transform, involving integration over planes parallel to
the boundary. For successful application of this method several nontrivial
hypergeometric function relations are also derived.Comment: 20 pagess, LateX fil
Finite VEVs from a Large Distance Vacuum Wave Functional
We show how to compute vacuum expectation values from derivative expansions
of the vacuum wave functional. Such expansions appear to be valid only for
slowly varying fields, but by exploiting analyticity in a complex scale
parameter we can reconstruct the contribution from rapidly varying fields.Comment: 39 pages, 16 figures, LaTeX2e using package graphic
Heat-kernel coefficients for oblique boundary conditions
We calculate the heat-kernel coefficients, up to , for a U(1) bundle on
the 4-Ball for boundary conditions which are such that the normal derivative of
the field at the boundary is related to a first-order operator in boundary
derivatives acting on the field. The results are used to place restrictions on
the general forms of the coefficients. In the specific case considered, there
can be a breakdown of ellipticity.Comment: 9 pages, JyTeX. One reference added and minor corrections mad
The dual of Janus -:- an interface CFT
We propose and study a specific gauge theory dual of the smooth,
non-supersymmetric (and apparently stable) Janus solution of Type IIB
supergravity found in hep-th/0304129. The dual field theory is N=4 SYM theory
on two half-spaces separated by a planar interface with different coupling
constants in each half-space. We assume that the position dependent coupling
multiplies the operator L' which is the fourth descendent of the primary Tr(X^I
X^J) and closely related to the N=4 Lagrangian density. At the classical level
supersymmetry is broken explicitly, but SO(3,2) conformal symmetry is
preserved. We use conformal perturbation theory to study various correlation
functions to first and second order in the discontinuity of g^2_{YM},
confirming quantum level conformal symmetry. Certain quantities such as the
vacuum expectation value are protected to all orders in g^2_{YM}N, and we
find perfect agreement between the weak coupling value in the gauge theory and
the strong coupling gravity result. SO(3,2) symmetry requires vanishing vacuum
energy, =0, and this is confirmed in first order in the
discontinuity.Comment: 24 pages, 1 figure; references adde
Diffeomorphism invariant eigenvalue problem for metric perturbations in a bounded region
We suggest a method of construction of general diffeomorphism invariant
boundary conditions for metric fluctuations. The case of dimensional
Euclidean disk is studied in detail. The eigenvalue problem for the Laplace
operator on metric perturbations is reduced to that on -dimensional vector,
tensor and scalar fields. Explicit form of the eigenfunctions of the Laplace
operator is derived. We also study restrictions on boundary conditions which
are imposed by hermiticity of the Laplace operator.Comment: LATeX file, no figures, no special macro
Thermal Quantum Fields in Static Electromagnetic Backgrounds
We present and discuss, at a general level, new mathematical results on the
spatial nonuniformity of thermal quantum fields coupled minimally to static
background electromagnetic potentials. Two distinct examples are worked through
in some detail: uniform (parallel and perpendicular) background electric and
magnetic fields coupled to a thermal quantum scalar field.Comment: 22 page
Worldline approach to quantum field theories on flat manifolds with boundaries
We study a worldline approach to quantum field theories on flat manifolds
with boundaries. We consider the concrete case of a scalar field propagating on
R_+ x R^{D-1} which leads us to study the associated heat kernel through a one
dimensional (worldline) path integral. To calculate the latter we map it onto
an auxiliary path integral on the full R^D using an image charge. The main
technical difficulty lies in the fact that a smooth potential on R_+ x R^{D-1}
extends to a potential which generically fails to be smooth on R^D. This
implies that standard perturbative methods fail and must be improved. We
propose a method to deal with this situation. As a result we recover the known
heat kernel coefficients on a flat manifold with geodesic boundary, and compute
two additional ones, A_3 and A_{7/2}. The calculation becomes sensibly harder
as the perturbative order increases, and we are able to identify the complete
A_{7/2} with the help of a suitable toy model. Our findings show that the
worldline approach is viable on manifolds with boundaries. Certainly, it would
be desirable to improve our method of implementing the worldline approach to
further simplify the perturbative calculations that arise in the presence of
non-smooth potentials.Comment: 19 pages, 6 figures. Minor rephrasing of a few sentences, references
added. Version accepted by JHE
Four-Dimensional Superconformal Theories with Interacting Boundaries or Defects
We study four-dimensional superconformal field theories coupled to
three-dimensional superconformal boundary or defect degrees of freedom.
Starting with bulk N=2, d=4 theories, we construct abelian models preserving
N=2, d=3 supersymmetry and the conformal symmetries under which the
boundary/defect is invariant. We write the action, including the bulk terms, in
N=2, d=3 superspace. Moreover we derive Callan-Symanzik equations for these
models using their superconformal transformation properties and show that the
beta functions vanish to all orders in perturbation theory, such that the
models remain superconformal upon quantization. Furthermore we study a model
with N=4 SU(N) Yang-Mills theory in the bulk coupled to a N=4, d=3
hypermultiplet on a defect. This model was constructed by DeWolfe, Freedman and
Ooguri, and conjectured to be conformal based on its relation to an AdS
configuration studied by Karch and Randall. We write this model in N=2, d=3
superspace, which has the distinct advantage that non-renormalization theorems
become transparent. Using N=4, d=3 supersymmetry, we argue that the model is
conformal.Comment: 30 pages, 4 figures, AMSLaTeX, revised comments on Chern-Simons term,
references adde
Smeared heat-kernel coefficients on the ball and generalized cone
We consider smeared zeta functions and heat-kernel coefficients on the
bounded, generalized cone in arbitrary dimensions. The specific case of a ball
is analysed in detail and used to restrict the form of the heat-kernel
coefficients on smooth manifolds with boundary. Supplemented by conformal
transformation techniques, it is used to provide an effective scheme for the
calculation of the . As an application, the complete coefficient
is given.Comment: 23 pages, JyTe
The heat kernel coefficient for oblique boundary conditions
We present a method for the calculation of the heat kernel
coefficient of the heat operator trace for a partial differential operator of
Laplace type on a compact Riemannian manifold with oblique boundary conditions.
Using special case evaluations, restrictions are put on the general form of the
coefficients, which, supplemented by conformal transformation techniques,
allows the entire smeared coefficient to be determined.Comment: 30 pages, LaTe
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