409 research outputs found
Composite operators and form factors in N=4 SYM
We construct the most general composite operators of N = 4 SYM in Lorentz
harmonic chiral ( twistor) superspace. The operators are built from
the SYM supercurvature which is nonpolynomial in the chiral gauge
prepotentials. We reconstruct the full nonchiral dependence of the
supercurvature. We compute all tree-level MHV form factors via the LSZ
redcution procedure with on-shell states made of the same supercurvature.Comment: 32 page
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
Short representations of SU(2,2/N) and harmonic superspace analyticity
We consider the harmonic superspaces associated to SU(2,2/N) superconformal
algebras. For arbitrary N, we show that massless representations, other than
the chiral ones, correspond to [N/2] ``elementary'' ultrashort analytic
superfields whose first component is a scalar in the k antisymmetric irrep of
SU(N) (k=1... [N/2]) with top spin . For
N=2n we analyze UIR's obtained by tensoring the self-conjugate ultrashort
multiplet = (n/2,0) and show that N-1 different basic
products give rise to all possible UIR's with residual shortening.Comment: references adde
N=4 super-Yang-Mills in LHC superspace. Part I: Classical and quantum theory
We present a formulation of the maximally supersymmetric N=4 gauge theory in
Lorentz harmonic chiral (LHC) superspace. It is closely related to the twistor
formulation of the theory but employs the simpler notion of Lorentz harmonic
variables. They parametrize a two-sphere and allow us to handle efficiently
infinite towers of higher-spin auxiliary fields defined on ordinary space-time.
In this approach the chiral half of N=4 supersymmetry is manifest. The other
half is realized non-linearly and the algebra closes on shell. We give a
straightforward derivation of the Feynman rules in coordinate space. We show
that the LHC formulation of the N=4 super-Yang-Mills theory is remarkably
similar to the harmonic superspace formulation of the N=2 gauge and
hypermultiplet matter theories. In the twin paper arXiv:1601.06804 we apply the
LHC formalism to the study of the non-chiral multipoint correlation functions
of the N=4 stress-tensor supermultiplet.Comment: 51 pages, 4 figures; v2: Appendix B on the propagators in momentum
space added. A more detailed comparison with the twistor approach given in
Appendix
Demystifying the twistor construction of composite operators in N=4 super-Yang-Mills theory
We explain some details of the construction of composite operators in N=4 SYM
that we have elaborated earlier in the context of Lorentz harmonic chiral (LHC)
superspace. We give a step-by-step elementary derivation and show that the
result coincides with the recent hypothesis put forward in arXiv:1603.04471
within the twistor approach. We provide the appropriate LHC-to-twistors
dictionary.Comment: 10 page
N=4 super-Yang-Mills in LHC superspace. Part II: Non-chiral correlation functions of the stress-tensor multiplet
We study the multipoint super-correlation functions of the full non-chiral
stress-tensor multiplet in N=4 super-Yang-Mills theory in the Born
approximation. We derive effective supergraph Feynman rules for them.
Surprisingly, the Feynman rules for the non-chiral correlators are obtained
from those for the chiral correlators by a simple Grassmann shift of the
space-time variables. We rely on the formulation of the theory in Lorentz
harmonic chiral (LHC) superspace elaborated in the twin paper arXiv:1601.06803.
In this approach only the chiral half of the supersymmetry is manifest. The
other half is realized by nonlinear and nonlocal transformations of the LHC
superfields. However, at Born level only the simple linear part of the
transformations is relevant. It corresponds to effectively working in the
self-dual sector of the theory. Our method is also applicable to a wider class
of supermultiplets like all the half-BPS operators and the Konishi multiplet.Comment: 66 pages, 16 figures; v2: Appendix F on the quantization in a
Lorentz-covariant gauge adde
Conformal primaries of OSp(8/4,R) and BPS states in AdS4
We derive short UIR's of the OSp(8/4,R) superalgebra of 3d N=8 superconformal
field theories by the requirement that the highest weight states are
annihilated by a subset of the super-Poincare odd generators. We then find a
superfield realization of these BPS saturated UIR's as "composite operators" of
the two basic ultrashort "supersingleton" multiplets. These representations are
the AdS4 analogue of BPS states preserving different fractions of supersymmetry
and are therefore suitable to classify perturbative and non-perturbative
excitations of M-theory compactifications.Comment: refrences adde
Representations of (1,0) and (2,0) superconformal algebras in six dimensions: massless and short superfields
We construct unitary representations of (1,0) and (2,0) superconformal
algebras in six dimensions by using superfields defined on harmonic superspaces
with coset manifolds USp(2n)/[U(1)]^n, n=1,2. In the spirit of the AdS_7/CFT_6
correspondence massless conformal fields correspond to "supersingletons" in
AdS_7. By tensoring them we produce all short representations corresponding to
1/2 and 1/4 BPS anti-de Sitter bulk states of which "massless bulk"
representations are particular cases.Comment: references adde
Superconformal interpretation of BPS states in AdS geometries
We carry out a general analysis of the representations of the superconformal
algebras SU(2,2/N), OSp(8/4,R) and OSp(8^*/4) and give their realization in
superspace. We present a construction of their UIR's by multiplication of the
different types of massless superfields ("supersingletons"). Particular
attention is paid to the so-called "short multiplets". Representations
undergoing shortening have "protected dimension" and correspond to BPS states
in the dual supergravity theory in anti-de Sitter space. These results are
relevant for the classification of multitrace operators in boundary conformally
invariant theories as well as for the classification of AdS black holes
preserving different fractions of supersymmetry.Comment: The sections on 6 and 3 dimensions considerably extended; important
new references added; misprints correcte
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