1,182 research outputs found
Instantons on ALE spaces and Super Liouville Conformal Field Theories
We provide evidence that the conformal blocks of N=1 super Liouville
conformal field theory are described in terms of the SU(2) Nekrasov partition
function on the ALE space O_{P^1}(-2).Comment: 10 page
Structure constants of planar N =4 Yang Mills at one loop
We study structure constants of gauge invariant operators in planar N=4
Yang-Mills at one loop with the motivation of determining features of the
string dual of weak coupling Yang-Mills. We derive a simple renormalization
group invariant formula characterizing the corrections to structure constants
of any primary operator in the planar limit. Applying this to the scalar SO(6)
sector we find that the one loop corrections to structure constants of gauge
invariant operators is determined by the one loop anomalous dimension
Hamiltonian in this sector. We then evaluate the one loop corrections to
structure constants for scalars with arbitrary number of derivatives in a given
holomorphic direction. We find that the corrections can be characterized by
suitable derivatives on the four point tree function of a massless scalar with
quartic coupling. We show that individual diagrams violating conformal
invariance can be combined together to restore it using a linear inhomogeneous
partial differential equation satisfied by this function.Comment: 52 pages, 12 figures, Typos fixed, reference adde
Towards a string bit formulation of N=4 super Yang-Mills
We show that planar cal N=4 Yang-Mills theory at zero 't Hooft coupling can
be efficiently described in terms of 8 bosonic and 8 fermionic oscillators. We
show that these oscillators can serve as world-sheet variables, the string
bits, of a discretized string. There is a one to one correspondence between the
on shell gauge invariant words of the free Y-M theory and the states in the
oscillators' Hilbert space, obeying a local gauge and cyclicity constraints.
The planar two-point functions and the three-point functions of all gauge
invariant words are obtained by the simple delta-function overlap of the
corresponding discrete string world sheet. At first order in the 't Hooft
coupling, i.e. at one-loop in the Y-M theory, the logarithmic corrections of
the planar two-point and the three-point functions can be incorporated by
nearest neighbour interactions among the discretized string bits. In the SU(2)
sub-sector we show that the one-loop corrections to the structure constants can
be uniquely determined by the symmetries of the bit picture. For the SU(2)
sub-sector we construct a gauged, linear, discrete world-sheet model for the
oscillators, with only nearest neighbour couplings, which reproduces the
anomalous dimension Hamiltonian up to two loops. This model also obeys BMN
scaling to all loops.Comment: 64 pages, 6 figures, typos fixed, references adde
Correlation functions, null polygonal Wilson loops, and local operators
We consider the ratio of the correlation function of n+1 local operators over
the correlator of the first n of these operators in planar N=4 super-Yang-Mills
theory, and consider the limit where the first n operators become pairwise null
separated. By studying the problem in twistor space, we prove that this is
equivalent to the correlator of a n-cusp null polygonal Wilson loop with the
remaining operator in general position, normalized by the expectation value of
the Wilson loop itself, as recently conjectured by Alday, Buchbinder and
Tseytlin. Twistor methods also provide a BCFW-like recursion relation for such
correlators. Finally, we study the natural extension where n operators become
pairwise null separated with k operators in general position. As an example, we
perform an analysis of the resulting correlator for k=2 and discuss some of the
difficulties associated to fixing the correlator completely in the strong
coupling regime.Comment: 34 pages, 6 figures. v2: typos corrected and references added; v3:
published versio
On correlation functions of Wilson loops, local and non-local operators
We discuss and extend recent conjectures relating partial null limits of
correlation functions of local gauge invariant operators and the expectation
value of null polygonal Wilson loops and local gauge invariant operators. We
point out that a particular partial null limit provides a strategy for the
calculation of the anomalous dimension of short twist-two operators at weak and
strong coupling.Comment: 29 pages, 8 figure
Gravitational F-terms of N=1 Supersymmetric SU(N) Gauge Theories
We use the generalized Konishi anomaly equations and R-symmetry anomaly to
compute the exact perturbative and non-perturbative gravitational F-terms of
four-dimensional N=1 supersymmetric gauge theories. We formulate the general
procedure for computation and consider chiral and non-chiral SU(N) gauge
theories.Comment: 25 pages, v2: minor changes in section 4, references adde
Large spin systematics in CFT
20 pages; v2: version published in JHEPUsing conformal field theory (CFT) arguments we derive an infinite number of constraints on the large spin expansion of the anomalous dimensions and structure constants of higher spin operators. These arguments rely only on analiticity, unitarity, crossing-symmetry and the structure of the conformal partial wave expansion. We obtain results for both, perturbative CFT to all order in the perturbation parameter, as well as non-perturbatively. For the case of conformal gauge theories this provides a proof of the reciprocity principle to all orders in perturbation theory and provides a new "reciprocity" principle for structure constants. We argue that these results extend also to non-conformal theories.Peer reviewe
Wilson Loops @ 3-Loops in Special Kinematics
We obtain a compact expression for the octagon MHV amplitude / Wilson loop at
3 loops in planar N=4 SYM and in special 2d kinematics in terms of 7 unfixed
coefficients. We do this by making use of the cyclic and parity symmetry of the
amplitude/Wilson loop and its behaviour in the soft/collinear limits as well as
in the leading term in the expansion away from this limit. We also make a
natural and quite general assumption about the functional form of the result,
namely that it should consist of weight 6 polylogarithms whose symbol consists
of basic cross-ratios only (and not functions thereof). We also describe the
uplift of this result to 10 points.Comment: 26 pages. Typos correcte
Gravitational F-terms of N=1 Supersymmetric Gauge Theories
We consider four-dimensional N=1 supersymmetric gauge theories in a
supergravity background. We use generalized Konishi anomaly equations and
R-symmetry anomaly to compute the exact perturbative and non-perturbative
gravitational F-terms. We study two types of theories: The first model breaks
supersymmetry dynamically, and the second is based on a gauge group. The
results are compared with the corresponding vector models. We discuss the
diagrammatic expansion of the theory.Comment: LaTeX2e, 23 pages, 2 figures. Added a reference and converted into
JHEP styl
On Fermionic T-duality of Sigma modes on AdS backgrounds
We study the fermionic T-duality symmetry of integrable Green-Schwarz sigma
models on AdS backgrounds. We show that the sigma model on
background is self-dual under fermionic T-duality. We also construct new
integrable sigma models on . These backgrounds could be
realized as supercosets of SU supergroups for arbitrary , but could also be
realized as supercosets of OSp supergroups for . We find that the
supercosets based on SU supergroups are self-dual under fermionic T-duality,
while the supercosets based on OSp supergroups are not. However, the reasons of
OSp supercosets being not self-dual under fermionic T-duality are different.
For case, corresponding to background, the
failure is due to the singular fermionic quadratic terms, just like
case. For case, the failure is due to the
shortage of right number of -symmetry to gauge away the fermionic
degrees of freedom, even though the fermionic quadratic term is not singular
any more. More general, for the supercosets of the OSp supergroups with
superalgebra , including and
backgrounds, the sigma models are not self-dual under fermionic T-duality as
well, obstructed by the -symmetry.Comment: 17 pages; Clarfications on kappa symmetries, references
added;Published versio
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