1,894 research outputs found
Tachyon Stabilization in the AdS/CFT Correspondence
We consider duality between type 0B string theory on and
the planar CFT on electric D3-branes coincident with magnetic
D3-branes. It has been argued that this theory is stable up to a critical value
of the `t Hooft coupling but is unstable beyond that point. We suggest that
from the gauge theory point of view the development of instability is
associated with singularity in the dimension of the operator corresponding to
the tachyon field via the AdS/CFT map. Such singularities are common in large
theories because summation over planar graphs typically has a finite radius
of convergence. Hence we expect transitions between stability and instability
for string theories in AdS backgrounds that are dual to certain large gauge
theories: if there are tachyons for large AdS radius then they may be
stabilized by reducing the radius below a critical value of order the string
scale.Comment: 10 pages, harvmac; v2: 1 minor clarification, 1 reference adde
TASI Lectures: Introduction to the AdS/CFT Correspondence
This is an introductory review of the AdS/CFT correspondence and of the ideas
that led to its formulation. We show how comparison of stacks of D3-branes with
corresponding supergravity solutions leads to dualities between conformal large
gauge theories in 4 dimensions and string backgrounds of the form
where is an Einstein manifold. The gauge invariant
chiral operators of the field theory are in one-to-one correspondence with the
supergravity modes, and their correlation functions at strong `t Hooft coupling
are determined by the dependence of the supergravity action on AdS boundary
conditions. The simplest case is when is a 5-sphere and the dual gauge
theory is the supersymmetric SU(N) Yang-Mills theory. We also
discuss D3-branes on the conifold corresponding to being a coset space
. This background is dual to a certain superconformal field theory with gauge group .Comment: Lectures at TASI '99, Boulder, June 1999; 36 pages, LaTeX; v2:
corrected factor of 2 in eq. (9) and related factor
A universal result on central charges in the presence of double-trace deformations
We study large N conformal field theories perturbed by relevant double-trace
deformations. Using the auxiliary field trick, or Hubbard-Stratonovich
transformation, we show that in the infrared the theory flows to another CFT.
The generating functionals of planar correlators in the ultraviolet and
infrared CFT's are shown to be related by a Legendre transform. Our main result
is a universal expression for the difference of the scale anomalies between the
ultraviolet and infrared fixed points, which is of order 1 in the large N
expansion. Our computations are entirely field theoretic, and the results are
shown to agree with predictions from AdS/CFT. We also remark that a certain
two-point function can be computed for all energy scales on both sides of the
duality, with full agreement between the two and no scheme dependence.Comment: 15 pages, latex2e, no figures. v2: references adde
Interpolating between and
We study the dimensional continuation of the sphere free energy in conformal
field theories. In continuous dimension we define the quantity , where is the path integral of the Euclidean CFT on
the -dimensional round sphere. smoothly interpolates between
times the -anomaly coefficient in even , and
times the sphere free energy in odd . We calculate
in various examples of unitary CFT that can be continued to
non-integer dimensions, including free theories, double-trace deformations at
large , and perturbative fixed points in the expansion. For all
these examples is positive, and it decreases under RG flow. Using
perturbation theory in the coupling, we calculate in the
Wilson-Fisher fixed point of the vector model in to order
. We use this result to estimate the value of in the
3-dimensional Ising model, and find that it is only a few percent below of
the free conformally coupled scalar field. We use similar methods to estimate
the values for the Gross-Neveu model in and the model
in . Finally, we carry out the dimensional continuation of interacting
theories with 4 supercharges, for which we suggest that may be
calculated exactly using an appropriate version of localization on . Our
approach provides an interpolation between the -maximization in and
the -maximization in .Comment: 41 pages, 4 figures. v4: Eqs. (1.6), (4.13) and (5.37) corrected;
footnote 9 added discussing the Euler density counterter
Matrix Model Approach to Non-critical Superstrings
We apply light-cone quantization to a dimensional supersymmetric field
theory of large N matrices. We provide some preliminary numerical evidence that
when the coupling constant is tuned to a critical value, this model describes a
2+1 dimensional non-critical superstring.Comment: 11 pages, 3 Encapsulated Postscript figures. uses psfig.sty
(available from http://xxx.lanl.gov/ftp/hep-th/papers/macros
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