272 research outputs found
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
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
Schwarzschild Black Holes in Various Dimensions from Matrix Theory
In a recent paper it was shown that the properties of Schwarzschild black
holes in 8 dimensions are correctly described up to factors of order unity by
Matrix theory compactified on T^3. Here we consider compactifications on tori
of general dimension d. Although in general little is known about the relevant
d+1 dimensional theories on the dual tori, there are hints from their
application to near-extreme parallel Dirichlet d-branes. Using these hints we
get the correct mass-entropy scaling for Schwarzschild black holes in (11-d)
dimensions.Comment: 7 pages, latex; a typo corrected (version to appear in Physics
Letters B
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
One Loop Tests of Higher Spin AdS/CFT
Vasiliev's type A higher spin theories in AdS4 have been conjectured to be
dual to the U(N) or O(N) singlet sectors in 3-d conformal field theories with
N-component scalar fields. We compare the O(N^0) correction to the 3-sphere
free energy F in the CFTs with corresponding calculations in the higher spin
theories. This requires evaluating a regularized sum over one loop vacuum
energies of an infinite set of massless higher spin gauge fields in Euclidean
AdS4. For the Vasiliev theory including fields of all integer spin and a scalar
with Delta=1 boundary condition, we show that the regularized sum vanishes.
This is in perfect agreement with the vanishing of subleading corrections to F
in the U(N) singlet sector of the theory of N free complex scalar fields. For
the minimal Vasiliev theory including fields of only even spin, the regularized
sum remarkably equals the value of F for one free real scalar field. This
result may agree with the O(N) singlet sector of the theory of N real scalar
fields, provided the coupling constant in the Vasiliev theory is identified as
G_N ~ 1/(N-1). Similarly, consideration of the USp(N) singlet sector for N
complex scalar fields, which we conjecture to be dual to the husp(2;0|4)
Vasiliev theory, requires G_N ~ 1/(N+1). We also test the higher spin AdS3/CFT2
conjectures by calculating the regularized sum over one loop vacuum energies of
higher spin fields in AdS3. We match the result with the O(N^0) term in the
central charge of the W_N minimal models; this requires a certain truncation of
the CFT operator spectrum so that the bulk theory contains two real scalar
fields with the same boundary conditions.Comment: 20 pages. v3: minor corrections, version published in JHE
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