2,387 research outputs found
Conjectures for Large N Superconformal N=4 Chiral Primary Four Point Functions
An expression for the four point function for half-BPS operators belonging to
the [0,p,0] SU(4) representation in N=4 superconformal theories at strong
coupling in the large N limit is suggested for any p. It is expressed in terms
of the four point integrals defined by integration over AdS_5 and agrees with,
and was motivated by, results for p=2,3,4 obtained via the AdS/CFT
correspondence. Using crossing symmetry and unitarity, the detailed form is
dictated by the requirement that at large N the contribution of long multiplets
with twist less than 2p, which do not have anomalous dimensions, should cancel
corresponding free field contributions.Comment: 50 pages, 1 figure, uses harvmac, version 2 extra reference, minor
change
Quantum Strings and Bethe Equations
I briefly review the recently proposed construction of the Bethe ansatz which
diagonalizes the Hamiltonian for quantum strings on AdS_5\times S^5 at large
tension and restricted to the large charge states from a closed su(2)
subsector.Comment: Latex, 6 pages, Talk delivered at RTN Workshop on the Quantum
Structure of Space-time and the Geometric Nature of Fundamental Interactions
and EXT Workshop on Fundamental Interactions and the Structure of Spacetime,
Kolymbari, Crete, Greece, 5-10 Sep 200
Four-point correlators of BPS operators in N=4 SYM at order g^4
We study the large N degeneracy in the structure of the four-point amplitudes
of 1/2-BPS operators of arbitrary weight k in perturbative N=4 SYM theory. At
one loop (order g^2) this degeneracy manifests itself in a smaller number of
independent conformal invariant functions describing the amplitude, compared to
AdS_5 supergravity results. To study this phenomenon at the two-loop level
(order g^4) we consider a particular N=2 hypermultiplet projection of the
general N=4 amplitude. Using the formalism of N=2 harmonic superspace we then
explicitly compute this four-point correlator at two loops and identify the
corresponding conformal invariant functions. In the cases of 1/2-BPS operators
of weight k=3 and k=4 the one-loop large N degeneracy is lifted by the two-loop
corrections. However, for weight k > 4 the degeneracy is still there at the
two-loop level. This behavior suggests that for a given weight k the degeneracy
will be removed if perturbative corrections of sufficiently high order are
taken into account. These results are in accord with the AdS/CFT duality
conjecture.Comment: 45 pages, latex, 14 figure
Superconformal Ward Identities and their Solution
Superconformal Ward identities are derived for the the four point functions
of chiral primary BPS operators for superconformal symmetry in four
dimensions. Manipulations of arbitrary tensorial fields are simplified by
introducing a null vector so that the four point functions depend on two
internal -symmetry invariants as well as two conformal invariants. The
solutions of these identities are interpreted in terms of the operator product
expansion and are shown to accommodate long supermultiplets with free scale
dimensions and also short and semi-short multiplets with protected dimensions.
The decomposition into -symmetry representations is achieved by an expansion
in terms of two variable harmonic polynomials which can be expressed also in
terms of Legendre polynomials. Crossing symmetry conditions on the four point
functions are also discussed.Comment: 73 pages, plain Tex, uses harvmac, version 2, extra reference
Conformal Partial Wave Expansions for N=4 Chiral Four Point Functions
The conformal partial wave analysis of four point functions of half BPS
operators belonging to the SU(4) [0,p,0] representation is undertaken for
p=2,3,4. Using the results of N=4 superconformal Ward identities the
contributions from protected short and semi-short multiplets are identified in
terms of the free field theory. In the large N limit contributions
corresponding to long multiplets with twist up to 2p-2 are absent. The
anomalous dimensions for twist two singlet multiplets are found to order g^4
and agree with other perturbative calculations. Results for twist four and six
are also found.Comment: 53 pages, uses harvmac, includes 1 figure, version 2 some corrections
and minor extensions, version 3 some further corrections, version 4 as to be
publishe
Superconformal Symmetry, Correlation Functions and the Operator Product Expansion
Superconformal transformations are derived for the \N=4\N=2$ or 4
superconformal identities are derived for the functions of the two conformal
invariants appearing in the four point function for the chiral primary
operator. These are solved in terms of a single arbitrary function of the two
conformal invariants and one or three single variable functions. The results
are applied to the operator product expansion using the exact formula for the
contribution of an operator in the operator product expansion in four
dimensions to a scalar four point function. Explicit expressions representing
exactly the contribution of both long and possible short supermultiplets to the
chiral primary four point function are obtained. These are applied to give the
leading perturbative and large N corrections to the scale dimensions of long
supermultiplets.Comment: 75 pages, plain TeX file using harvmac; revised version, minor
corrections and extra referenc
The Bound State S-Matrix for AdS5 x S5 Superstring
We determine the S-matrix that describes scattering of arbitrary bound states
in the light-cone string theory in AdS5 x S5. The corresponding construction
relies on the Yangian symmetry and the superspace formalism for the bound state
representations. The basic analytic structure supporting the S-matrix entries
turns out to be the hypergeometric function 4F3. We show that for particular
bound state numbers it reproduces all the scattering matrices previously
obtained in the literature. Our findings should be relevant for the TBA and
Luescher approaches to the finite-size spectral problem. They also shed some
light on the construction of the universal R-matrix for the centrally-extended
psu(2|2) superalgebra.Comment: 37 pages, 2 figures, v2: typos correcte
On Exceptional Non-renormalization Properties Of N=4 SYM
We discuss non-renormalization properties of some composite operators in N=4
supersymmetric Yang-Mills theory.Comment: Contribution to the proceedings of the conference SUSY01 held in
Dubna, June 2001; Latex, 4
Lifting asymptotic degeneracies with the Mirror TBA
We describe a qualitative feature of the AdS_5 x S^5 string spectrum which is
not captured by the asymptotic Bethe ansatz. This is reflected by an enhanced
discrete symmetry in the asymptotic limit, whereby extra energy degeneracy
enters the spectrum. We discuss how finite size corrections should lift this
degeneracy, through both perturbative (Luscher) and non-perturbative
approaches (the Mirror TBA), and illustrate this explicitly on two such
asymptotically degenerate states.Comment: v3, 20 pages, 1 figure, 2 tables, as publishe
Temperature quantization from the TBA equations
We analyze the Thermodynamic Bethe Ansatz equations for the mirror model
which determine the ground state energy of the light-cone AdS_5 x S^5
superstring living on a cylinder. The light-cone momentum of string is equal to
the circumference of the cylinder, and is identified with the inverse
temperature of the mirror model. We show that the natural requirement of the
analyticity of the Y-functions leads to the quantization of the temperature of
the mirror model which has never been observed in any other models.Comment: 1+14 pages, v2: a paragraph added in section 2.
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