1,034 research outputs found
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
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
Comments on the Mirror TBA
We discuss various aspects of excited state TBA equations describing the
energy spectrum of the AdS_5 \times S^5 strings and, via the AdS/CFT
correspondence, the spectrum of scaling dimensions of N = 4 SYM local
operators. We observe that auxiliary roots which are used to partially
enumerate solutions of the Bethe-Yang equations do not play any role in
engineering excited state TBA equations via the contour deformation trick. We
further argue that the TBA equations are in fact written not for a particular
string state but for the whole superconformal multiplet, and, therefore, the
psu(2,2|4) invariance is built in into the TBA construction.Comment: 28 pages, 1 figure, v2: misprints are correcte
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
Exceptional Operators in N=4 super Yang-Mills
We consider one particularly interesting class of composite gauge-invariant
operators in N=4 super Yang-Mills theory. An exceptional feature of these
operators is that in the Thermodynamic Bethe Ansatz approach the one-loop
rapidities of the constituent magnons are shown to be exact in the 't Hooft
coupling constant. This is used to propose the mirror TBA description for these
operators. The proposal is shown to pass several non-trivial checks.Comment: 40 pages, 2 figures, 1 attached Mathematica noteboo
Perturbative and instanton corrections to the OPE of CPOs in N=4 SYM_4
We study perturbative and instanton corrections to the Operator Product
Expansion of the lowest weight Chiral Primary Operators of N=4 SYM_4. We
confirm the recently observed non-renormalization of various operators (notably
of the double-trace operator with dimension 4 in the 20 irrep of SU(4)), that
appear to be unprotected by unitarity restrictions. We demonstrate the
splitting of the free-field theory stress tensor and R-symmetry current in
supermultiplets acquiring different anomalous dimensions in perturbation theory
and argue that certain double-trace operators also undergo a perturbative
splitting into operators dual to string and two-particle gravity states
respectively. The instanton contributions affect only those double-trace
operators that acquire finite anomalous dimensions at strong coupling. For the
leading operators of this kind, we show that the ratio of their anomalous
dimensions at strong coupling to the anomalous dimensions due to instantons is
the same number.Comment: Latex, 26p, typos are removed, a strong-coupling anomalous dimension
of one of the double-trace operators is correcte
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