1,145 research outputs found

### 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

### 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

### On a Large N Degeneracy in N=4 SYM and the AdS/CFT Correspondence

We study the four-point correlator of 1/2-BPS operators of weight 4 in N=4
SYM, which are dual to massive KK modes in AdS_5 supergravity. General
field-theoretic arguments lead to a partially non-renormalized form of the
amplitude that depends on two a priori independent functions of the conformal
cross-ratios. We explicitly compute the amplitude in the large N limit at one
loop (order g^2) and in AdS_5 supergravity. Surprisingly, the one-loop result
shows that the two functions determining the amplitude coincide while in the
supergravity regime they are distinctly different. We discuss the possible
implications of this perturbative degeneracy for the AdS/CFT correspondence.Comment: 32 pages, 5 figures, LaTex, the Summary and Conclusions section
extended, references adde

### Two-loop commuting charges and the string/gauge duality

We briefly review the status quo of the application of integrable systems
techniques to the AdS/CFT correspondence in the large charge approximation, a
rapidly evolving topic. Intricate string and gauge computations of,
respectively, energies and scaling dimensions agree at the one and two-loop
level, but disagree starting from three loops. To add to this pattern, we
present further computations which demonstrate that for folded and circular
spinning strings the full tower of infinitely many hidden commuting charges,
responsible for the integrability, also agrees up to two, but not three, loops.Comment: 12 pages, Latex, contribution to 5th International Workshop on Lie
Theory and Its Applications in Physics, Varna, Bulgaria, 16-22 Jun 2003; v2:
references adde

### Scalar Quartic Effective Action on $AdS_5$

We review the recent results concerning the computation of cubic and quartic
couplings of scalar fields in type IIB supergravity on AdS_5\times S^5
background that are dual to (extended) chiral primary operators in N=4 SYM_4.
We discuss the vanishing of certain cubic and quartic couplings and
non-renormalization property of corresponding correlators in the conformal
field theoryComment: 6 pages, Latex, JHEP style; based on the talk by G. Arutyunov at the
TMR Meeting "Quantum Aspects of Gauge Theories, Supersymmetry and
Unification" held in Paris, September 199

### Integrable Hamiltonian for Classical Strings on AdS_5 x S^5

We find the Hamiltonian for physical excitations of the classical bosonic
string propagating in the AdS_5 x S^5 space-time. The Hamiltonian is obtained
in a so-called uniform gauge which is related to the static gauge by a 2d
duality transformation. The Hamiltonian is of the Nambu type and depends on two
parameters: a single S^5 angular momentum J and the string tension \lambda. In
the general case both parameters can be finite. The space of string states
consists of short and long strings. In the sector of short strings the large J
expansion with \lambda'=\lambda/J^2 fixed recovers the plane-wave Hamiltonian
and higher-order corrections recently studied in the literature. In the strong
coupling limit \lambda\to \infty, J fixed, the energy of short strings scales
as \sqrt[4]{\lambda} while the energy of long strings scales as \sqrt{\lambda}.
We further show that the gauge-fixed Hamiltonian is integrable by constructing
the corresponding Lax representation. We discuss some general properties of the
monodromy matrix, and verify that the asymptotic behavior of the quasi-momentum
perfectly agrees with the one obtained earlier for some specific cases.Comment: 30 pages, LaTex; v2: a few comments added, misprints corrected,
references adde

### 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

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