281 research outputs found
Non-renormalisation of extremal correlators in N=4 SYM theory
We show that extremal correlators of chiral primary operators in N=4
supersymmetric Yang-Mills theory with SU(N) gauge group are neither
renormalised at first order in perturbation theory nor receive contribution
from any instanton sector at leading order in the semiclassical expansion. This
lends support to the strongest version of a new prediction recently put forward
on the basis of the AdS/SCFT correspondence.Comment: 13 pages, LaTeX2e; definition of extremal correlators moved to the
introduction, references added; final version to appear in Physics Letters
Holography and the Higgs branch of N=2 SYM theories
We present a proposal for the description of the Higgs branch of
four-dimensional N=2 supersymmetric Yang-Mills theories in the context of the
AdS/CFT correspondence. We focus on a finite Sp(N) N=2 theory arising as dual
of a configuration of N D3-branes in the vicinity of four D7-branes and an
orientifold 7-plane in type I' string theory. The field theory contains
hypermultiplets in the second rank anti-symmetric and in the fundamental
representations. The Higgs branch has a dual description in terms of gauge
field configurations with non-zero instanton number on the world-volume of the
D7-branes. In this setting the non-renormalisation of the metric on the Higgs
branch implies constraints on the alpha' corrections to the D7-brane effective
action, including couplings to the curvature and five-form field strength. In
the second part of the paper we discuss non-renormalisation properties of BPS
Wilson lines, which are closely related to the physics of the Higgs branch.
Using a formulation of the four-dimensional N=2 theory in terms of a
three-dimensional N=2 superspace we show that the expectation value of certain
Wilson-line operators with hypermultiplets at the end points is independent of
the length and thus coincides with the expectation value of the local operators
parametrising the Higgs branch.Comment: LaTeX, 29 pages, 1 figure; v2: minor corrections, one reference adde
Membranes from monopole operators in ABJM theory: large angular momentum and M-theoretic AdS_4/CFT_3
We consider states with large angular momentum to facilitate the study of the
M-theory regime of the AdS_4/CFT_3 correspondence. We study the duality between
M-theory in AdS_4xS^7/Z_k and the ABJM N=6 Chern-Simons-matter theory with
gauge group U(N)xU(N) and level k, taking N large and k of order 1. In this
regime the lack of an explicit formulation of M-theory in AdS_4xS^7/Z_k makes
the gravity side difficult, while the CFT is strongly coupled and the planar
approximation is not applicable. To overcome these difficulties, we focus on
states on the gravity side with large angular momentum J>>1 and identify the
dual operators in the CFT, thereby establishing the AdS/CFT dictionary in this
sector. Natural approximation schemes arise on both sides thanks to the
presence of the small parameter 1/J. On the AdS side, we use the matrix model
of M-theory on the maximally supersymmetric pp-wave background with matrices of
size J/k. A perturbative treatment of this matrix model provides a good
approximation to M-theory in AdS_4xS^7/Z_k when N^{1/3}<<J<<N^{1/2}. On the CFT
side, we study the theory on S^2xR with magnetic flux J/k. A Born-Oppenheimer
type expansion arises naturally for large J in spite of the theory being
strongly coupled. The energy spectra on the two sides agree at leading order.
This provides a non-trivial test of the AdS_4/CFT_3 correspondence including
near-BPS observables associated with membrane degrees of freedom, thus
verifying the duality beyond the previously studied sectors corresponding to
either BPS observables or the type IIA string regime.Comment: 67 pages, 5 figures; V2: minor changes, references adde
On membrane interactions and a three-dimensional analog of Riemann surfaces
Membranes in M-theory are expected to interact via splitting and joining
processes. We study these effects in the pp-wave matrix model, in which they
are associated with transitions between states in sectors built on vacua with
different numbers of membranes. Transition amplitudes between such states
receive contributions from BPS instanton configurations interpolating between
the different vacua. Various properties of the moduli space of BPS instantons
are known, but there are very few known examples of explicit solutions. We
present a new approach to the construction of instanton solutions interpolating
between states containing arbitrary numbers of membranes, based on a continuum
approximation valid for matrices of large size. The proposed scheme uses
functions on a two-dimensional space to approximate matrices and it relies on
the same ideas behind the matrix regularisation of membrane degrees of freedom
in M-theory. We show that the BPS instanton equations have a continuum
counterpart which can be mapped to the three-dimensional Laplace equation
through a sequence of changes of variables. A description of configurations
corresponding to membrane splitting/joining processes can be given in terms of
solutions to the Laplace equation in a three-dimensional analog of a Riemann
surface, consisting of multiple copies of R^3 connected via a generalisation of
branch cuts. We discuss various general features of our proposal and we also
present explicit analytic solutions.Comment: 64 pages, 17 figures. V2: An appendix, a figure and references added;
various minor changes and improvement
Mixing of the RR and NSNS sectors in the BMN limit
This paper concerns instanton contributions to two-point correlation
functions of BMN operators in N=4 supersymmetric Yang-Mills that vanish in
planar perturbation theory. Two-point functions of operators with even numbers
of fermionic impurities (dual to RR string states) and with purely scalar
impurities (dual to NSNS string states) are considered. This includes mixed RR
- NSNS two-point functions. The gauge theory correlation functions are shown to
respect BMN scaling and their behaviour is found to be in good agreement with
the corresponding D-instanton contributions to two-point amplitudes in the
maximally supersymmetric IIB plane-wave string theory. The string theory
calculation also shows a simple dependence of the mass matrix elements on the
mode numbers of states with an arbitrary number of impurities, which is
difficult to extract from the gauge theory. For completeness, a discussion is
also given of the perturbative mixing of two-impurity states in the RR and NSNS
sectors at the first non-planar level.Comment: latex, 29 pages, 4 figure
N=4 supersymmetric Yang-Mills theory and the AdS/SCFT correspondence
This dissertation reviews various aspects of the N=4 supersymmetric
Yang--Mills theory in particular in relation with the AdS/CFT correspondence.
The first two chapters are introductory. The first one contains a description
of the general properties of rigid supersymmetric theories in four dimensions
both at the classical and at the quantum level. The second chapter is a review
of the main properties of the N=4 SYM theory under consideration. Original
results are reported in chapters 3, 4 and 5. A systematic re-analysis of the
perturbative properties of the theory is presented in the third chapter. Two-,
three- and four-point Green functions of elementary fields are computed using
the component formulation and/or the superfield approach and subtleties related
to the gauge-fixing are pointed out. In the fourth chapter, after an
introduction to instanton calculus in supersymmetric gauge theories, the
computation of the one-instanton contributions to Green functions of gauge
invariant composite operators in the semiclassical approximation is reported.
The calculations of four-, eight- and sixteen-point Green functions of
operators in the supercurrent multiplet are reviewed in detail. The final
chapter is devoted to the AdS/SCFT correspondence. Some general aspects are
discussed. Then the attention is focused on the relation between instantons in
N=4 SYM and D-instanton effects in type IIB string theory. The comparison
between instanton contributions to Green functions of composite operators in
the boundary field theory and D-instanton generated terms in the amplitudes
computed in type IIB string theory is performed and agreement between these two
sources of non-perturbative effects is shown.Comment: 228 pages, Ph.D. thesis, LaTeX2e, uses the feynmp, fencyhdr, graphicx
and AMS package
Properties of the Konishi multiplet in N=4 SYM theory
We study perturbative and non-perturbative properties of the Konishi
multiplet in N=4 SYM theory in D=4 dimensions. We compute two-, three- and
four-point Green functions with single and multiple insertions of the lowest
component of the multiplet, and of the lowest component of the supercurrent
multiplet. These computations require a proper definition of the renormalized
operator and lead to an independent derivation of its anomalous dimension. The
O(g^2) value found in this way is in agreement with previous results. We also
find that instanton contributions to the above correlators vanish. From our
results we are able to identify some of the lowest dimensional gauge-invariant
composite operators contributing to the OPE of the correlation functions we
have computed. We thus confirm the existence of an operator belonging to the
representation 20', which has vanishing anomalous dimension at order g^2 and
g^4 in perturbation theory as well as at the non-perturbative level, despite
the fact that it does not obey any of the known shortening conditions.Comment: 23 pages, latex, no figure
On the logarithmic behaviour in N=4 SYM theory
We show that the logarithmic behaviour seen in perturbative and non
perturbative contributions to Green functions of gauge-invariant composite
operators in N=4 SYM with SU(N) gauge group can be consistently interpreted in
terms of anomalous dimensions of unprotected operators in long multiplets of
the superconformal group SU(2,2|4). In order to illustrate the point we analyse
the short-distance behaviour of a particularly simple four-point Green function
of the lowest scalar components of the N=4 supercurrent multiplet. Assuming the
validity of the Operator Product Expansion, we are able to reproduce the known
value of the one-loop anomalous dimension of the single-trace operators in the
Konishi supermultiplet. We also show that it does not receive any
non-perturbative contribution from the one-instanton sector. We briefly comment
on double- and multi-trace operators and on the bearing of our results on the
AdS/SCFT correspondence.Comment: 18 pages, Late
Instantons in supersymmetric Yang-Mills and D-instantons in IIB superstring theory
The one-instanton contributions to various correlation functions of
supercurrents in four-dimensional N=4 supersymmetric SU(2) Yang-Mills theory
are evaluated to the lowest order in perturbation theory.Expressions of the
same form are obtained from the leading effects of a single D-instanton
extracted from the IIB superstring effective action around the AdS5*S5
background. This is in line with the suggested AdS/Yang-Mills correspondence.
The relation between Yang--Mills instantons and D-instantons is further
confirmed by the explicit form of the classical D-instanton solution in the
AdS5*S5 background and its associated supermultiplet of zero modes.
Speculations are made concerning instanton effects in the large-N_c limit of
the SU(N_c) Yang-Mills theory.Comment: 41 pages, LaTeX. Typos corrected and minor clarifications adde
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