60 research outputs found
On Four-Point Functions of Half-BPS Operators in General Dimensions
We study four-point correlation functions of half-BPS operators of arbitrary
weight for all dimensions d=3,4,5,6 where superconformal theories exist. Using
harmonic superspace techniques, we derive the superconformal Ward identities
for these correlators and present them in a universal form. We then solve these
identities, employing Jack polynomial expansions. We show that the general
solution is parameterized by a set of arbitrary two-variable functions, with
the exception of the case d=4, where in addition functions of a single variable
appear. We also discuss the operator product expansion using recent results on
conformal partial wave amplitudes in arbitrary dimension.Comment: The discussion of the case d=6 expanded; references added/correcte
AdS/CFT for Four-Point Amplitudes involving Gravitino Exchange
In this paper we compute the tree-level four-point scattering amplitude of
two dilatini and two axion-dilaton fields in type IIB supergravity in AdS5 x
S5. A special feature of this process is that there is an "exotic" channel in
which there are no singleparticle poles. Another novelty is that this process
involves the exchange of a bulk gravitino. The amplitude is interpreted in
terms of N = 4 supersymmetric Yang-Mills theory at large 't Hooft coupling.
Properties of the Operator Product Expansion are used to analyze the various
contributions from single- and double-trace operators in the weak and strongly
coupled regimes, and to determine the anomalous dimensions of semi-short
operators. The analysis is particularly clear in the exotic channel, given the
absence of BPS states.Comment: 32 pages, 1 figure. Published Version. Minor change
Some Systematics of the Coupling Constant Dependence of N=4 Yang-Mills
The operator, O_\tau, that generates infinitesimal changes of the coupling
constant in N=4 Yang-Mills sits in the same supermultiplet as the
superconformal currents. We show how superconformal current Ward identities
determine a class of terms in the operator product expansion of O_\tau with any
other operator. In certain cases, this leads to constraints on the coupling
dependence of correlation functions in N=4 Yang-Mills. As an application, we
demonstrate the exact non-renormalization of two and certain three-point
correlation functions of BPS operators.Comment: 56 pages, LaTeX; amended and expanded arguments, added reference
Three-Point Functions of Quarter BPS Operators in N=4 SYM
In a recent paper hep-th/0109064, quarter-BPS chiral primaries were
constructed in the fully interacting four dimensional N=4 Super-Yang-Mills
theory with gauge group SU(N). These operators are annihilated by four
supercharges, and at order g^2 have protected scaling dimension and
normalization. Here, we compute three-point functions involving these
quarter-BPS operators along with half-BPS operators. The combinatorics of the
problem is rather involved, and we consider the following special cases: (1)
correlators of two half-BPS primaries with an arbitrary
chiral primary; (2) certain classes of and < quarter
quarter quarter > three-point functions; (3) three-point functions involving
the Delta
correlators with the special quarter-BPS operator made of single and double
trace operators only. The analysis in cases (1)-(3) is valid for general N,
while (4) is a large N approximation. Order g^2 corrections to all three-point
functions considered in this paper are found to vanish.
In the AdS/CFT correspondence, quarter-BPS chiral primaries are dual to
threshold bound states of elementary supergravity excitations. We present a
supergravity discussion of two- and three-point correlators involving these
bound states.Comment: 44 pages, Latex, eps figures, uses epsfig.sty; references adde
Operator mixing and three-point functions in N=4 SYM
We study the three-point functions between two BPS and one non-BPS local
gauge invariant operators in N=4 Super Yang-Mills theory. In particular we
show, in explicit 1-loop examples, that the operator mixing discussed in
arXiv:0810.0499 plays an important role in the computations of the correlators
and is necessary to cancel contributions that would violate the constraints
following from the superconformal and the bonus U(1)_Y symmetries. We analyse
the same type of correlators also at strong coupling by using the BMN limit of
the AdS_5xS^5 string theory. Again the mixing between states with different
types of impurities is crucial to ensure the cancellation of various amplitudes
that would violate the constraints mentioned above. However, on the string
side, we also find some examples of interactions between one non-BPS and two
BPS states that do not satisfy expectations based on the superconformal and the
bonus U(1)_Y symmetries.Comment: 28 pages, 5 figure
Supersymmetry of Tensionless Rotating Strings in AdS_5 x S^5, and Nearly-BPS Operators
It is shown that a class of rotating strings in AdS_5 x S^5 with SO(6)
angular momenta (J,J',J') preserve 1/8-supersymmetry for large J,J', in which
limit they are effectively tensionless; when J=0, supersymmetry is enhanced to
1/4. These results imply that recent checks of the AdS/CFT correspondence
actually test a nearly-BPS sector.Comment: 12 pages, no figures; v2: new section on CFT operators and new
references added, discussion section and acknowledgements modified, abstract
rephrashe
Supersymmetric null-surfaces
Single trace operators with the large R-charge in supersymmetric Yang-Mills
theory correspond to the null-surfaces in . We argue that the
moduli space of the null-surfaces is the space of contours in the
super-Grassmanian parametrizing the complex -dimensional subspaces of
the complex -dimensional space. The odd coordinates on this
super-Grassmanian correspond to the fermionic degrees of freedom of the
superstring.Comment: v4: added a reference to the earlier work; corrected the formula for
the stabilizer of the BMN vacuum; added the discussion of the complex
structure of the odd coordinates in Section 3.
On the spectrum of AdS/CFT beyond supergravity
We test the spectrum of string theory on AdS_5 x S^5 derived in
hep-th/0305052 against that of single-trace gauge invariant operators in free
N=4 super Yang-Mills theory. Masses of string excitations at critical tension
are derived by extrapolating plane-wave frequencies at g_{YM}=0 down to finite
J. On the SYM side, we present a systematic description of the spectrum of
single-trace operators and its reduction to PSU(2,2|4) superconformal primaries
via a refined Eratostenes' supersieve. We perform the comparison of the
resulting SYM/string spectra of charges and multiplicities order by order in
the conformal dimension \Delta up to \Delta=10 and find perfect agreement.
Interestingly, the SYM/string massive spectrum exhibits a hidden symmetry
structure larger than expected, with bosonic subgroup SO(10,2) and thirty-two
supercharges.Comment: 28 pages, LaTeX2
BRST approach to Lagrangian formulation for mixed-symmetry fermionic higher-spin fields
We construct a Lagrangian description of irreducible half-integer higher-spin
representations of the Poincare group with the corresponding Young tableaux
having two rows, on a basis of the BRST approach. Starting with a description
of fermionic higher-spin fields in a flat space of any dimension in terms of an
auxiliary Fock space, we realize a conversion of the initial operator
constraint system (constructed with respect to the relations extracting
irreducible Poincare-group representations) into a first-class constraint
system. For this purpose, we find auxiliary representations of the constraint
subsuperalgebra containing the subsystem of second-class constraints in terms
of Verma modules. We propose a universal procedure of constructing
gauge-invariant Lagrangians with reducible gauge symmetries describing the
dynamics of both massless and massive fermionic fields of any spin. No
off-shell constraints for the fields and gauge parameters are used from the
very beginning. It is shown that the space of BRST cohomologies with a
vanishing ghost number is determined only by the constraints corresponding to
an irreducible Poincare-group representation. To illustrate the general
construction, we obtain a Lagrangian description of fermionic fields with
generalized spin (3/2,1/2) and (3/2,3/2) on a flat background containing the
complete set of auxiliary fields and gauge symmetries.Comment: 41 pages, no figures, corrected typos, updated introduction, sections
5, 7.1, 7.2 with examples, conclusion with all basic results unchanged,
corrected formulae (3.27), (7.138), (7.140), added dimensional reduction part
with formulae (5.34)-(5.48), (7.8)-(7.10), (7.131)-(7.136), (7.143)-(7.164),
added Refs. 52, 53, 54, examples for massive fields developed by 2 way
Higher Spin Symmetry and N=4 SYM
We assemble the spectrum of single-trace operators in free N=4 SU(N) SYM
theory into irreducible representations of the Higher Spin symmetry algebra
hs(2,2|4). Higher Spin representations or YT-pletons are associated to Young
tableaux (YT) corresponding to representations of the symmetric group
compatible with the cyclicity of color traces. After turning on interactions,
YT-pletons decompose into infinite towers of representations of the
superconformal algebra PSU(2,2|4) and anomalous dimensions are generated. We
work out the decompositions of tripletons with respect to the N=4
superconformal algebra PSU(2,2|4) and compute their one anomalous dimensions at
large N. We then focus on operators/states sitting in semishort superconformal
multiplets. By passing them through a semishort-sieve that removes
superdescendants, we derive compact expressions for the partition function of
semishort primaries.Comment: 38 pages, no figures. v2: references adde
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