1,821 research outputs found
Amplitudes, Form Factors and the Dilatation Operator in SYM Theory
We study the form factor of a generic gauge-invariant local composite
operator in SYM theory. At tree level and for a minimal number
of external on-shell super fields, we find that the form factor precisely
yields the spin-chain picture of integrability in the language of scattering
amplitudes. Moreover, we compute the cut-constructible part of the one-loop
correction to this minimal form factor via generalised unitarity. From its UV
divergence, we obtain the complete one-loop dilatation operator of
SYM theory. Thus, we provide a field-theoretic derivation of a
relation between the one-loop dilatation operator and the four-point tree-level
amplitude which was observed earlier. We also comment on the implications of
our findings in the context of integrability.Comment: 39 pages, several figures, feynmp; v2: references added, typos
corrected; v3: references added, typos corrected, one explanation improved,
matches published versio
The Hagedorn temperature of AdS5/CFT4 at finite coupling via the Quantum Spectral Curve
Building on the recently established connection between the Hagedorn
temperature and integrability [Phys.Rev.Lett. 120 (2018) no.7, 071605], we show
how the Quantum Spectral Curve formalism can be used to calculate the Hagedorn
temperature of AdS5/CFT4 for any value of the 't Hooft coupling. We solve this
finite system of finite-difference equations perturbatively at weak coupling
and numerically at finite coupling. We confirm previous results at weak
coupling and obtain the previously unknown three-loop Hagedorn temperature. Our
finite-coupling results interpolate between weak and strong coupling and allow
us to extract the first perturbative order at strong coupling. Our results
indicate that the Hagedorn temperature for large 't Hooft coupling approaches
that of type IIB string theory in ten-dimensional Minkowski space.Comment: 7 page
The Hagedorn temperature of AdS5/CFT4 via integrability
We establish a framework for calculating the Hagedorn temperature of
AdS5/CFT4 via integrability. Concretely, we derive the thermodynamic Bethe
ansatz equations that yield the Hagedorn temperature of planar N=4 super
Yang-Mills theory at any value of the 't Hooft coupling. We solve these
equations perturbatively at weak coupling via the associated Y-system,
confirming the known results at tree-level and one-loop order as well as
deriving the previously unknown two-loop Hagedorn temperature. Finally, we
comment on solving the equations at finite coupling.Comment: 6 pages; v3: references and further clarification added, matches
journal versio
On a CFT limit of planar -deformed SYM theory
We show that an integrable four-dimensional non-unitary field theory that was
recently proposed as a certain limit of the -deformed
SYM theory is incomplete and not conformal -- not even in the planar limit. We
complete this theory by double-trace couplings and find conformal one-loop
fix-points when admitting respective complex coupling constants. These
couplings must not be neglected in the planar limit, as they can contribute to
planar multi-point functions. Based on our results for certain two-loop planar
anomalous dimensions, we propose tests of integrability.Comment: LaTeX, 3 pages, 1 Figur
Composite Operators in the Twistor Formulation of SYM Theory
We incorporate gauge-invariant local composite operators into the
twistor-space formulation of Super Yang-Mills theory. In this
formulation, the interactions of the elementary fields are reorganized into
infinitely many interaction vertices and we argue that the same applies to
composite operators. To test our definition of the local composite operators in
twistor space, we compute several corresponding form factors, thereby also
initiating the study of form factors using the position twistor-space
framework. Throughout this letter, we use the composite operator built from two
identical complex scalars as a pedagogical example; we treat the general case
in a follow-up paper.Comment: letter, 5 pages, 1 figur
Renormalization group coefficients and the S-matrix
We show how to use on-shell unitarity methods to calculate renormalization
group coefficients such as beta functions and anomalous dimensions. The central
objects are the form factors of composite operators. Their discontinuities can
be calculated via phase-space integrals and are related to corresponding
anomalous dimensions. In particular, we find that the dilatation operator,
which measures the anomalous dimensions, is given by minus the phase of the
S-matrix divided by pi. We illustrate our method using several examples from
Yang-Mills theory, perturbative QCD and Yukawa theory at one-loop level and
beyond.Comment: 25 pages, 4 figures; v2: explanations improved, references added,
matches journal versio
A Quantum Check of Non-Supersymmetric AdS/dCFT
Via a challenging field-theory computation, we confirm a supergravity
prediction for the non-supersymmetric D3-D7 probe-brane system with probe
geometry AdS_4 x S^2 x S^2, stabilized by fluxes. Supergravity predicts, in a
certain double-scaling limit, the value of the one-point functions of chiral
primaries of the dual defect version of N=4 SYM theory, where the fluxes
translate into SO(3) x SO(3)-symmetric, Lie-algebra-valued vacuum expectation
values for all six scalar fields. Using a generalization of the technique based
on fuzzy spherical harmonics developed for the related D3-D5 probe-brane
system, we diagonalize the resulting mass matrix of the field theory.
Subsequently, we calculate the planar one-loop correction to the vacuum
expectation values of the scalars in dimensional reduction and find that it is
UV finite and non-vanishing. We then proceed to calculating the one-loop
correction to the planar one-point function of any single-trace scalar operator
and explicitly evaluate this correction for a 1/2-BPS operator of length L at
two leading orders in the double-scaling limit, finding exact agreement with
the supergravity prediction.Comment: 33+14 pages, 5 figures; v2: typos corrected, reference added, version
published in JHE
Higgs-Boson Production at Small Transverse Momentum
Using methods from effective field theory, we have recently developed a
novel, systematic framework for the calculation of the cross sections for
electroweak gauge-boson production at small and very small transverse momentum
q_T, in which large logarithms of the scale ratio m_V/q_T are resummed to all
orders. This formalism is applied to the production of Higgs bosons in gluon
fusion at the LHC. The production cross section receives logarithmically
enhanced corrections from two sources: the running of the hard matching
coefficient and the collinear factorization anomaly. The anomaly leads to the
dynamical generation of a non-perturbative scale q_* ~ m_H
e^{-const/\alpha_s(m_H)} ~ 8 GeV, which protects the process from receiving
large long-distance hadronic contributions. We present detailed numerical
predictions for the transverse-momentum spectrum of the Higgs boson, finding
that it is quite insensitive to hadronic effects.Comment: 18 pages, 5 figures; v2: published version, includes a correction in
(8) and (22
Massive Boson Production at Small q_T in Soft-Collinear Effective Theory
We study the differential cross sections for electroweak gauge-boson and
Higgs production at small and very small transverse-momentum q_T. Large
logarithms are resummed using soft-collinear effective theory. The collinear
anomaly generates a non-perturbative scale q_*, which protects the processes
from receiving large long-distance hadronic contributions. A numerical
comparison of our predictions with data on the transverse-momentum distribution
in Z-boson production at the Tevatron and LHC is given.Comment: PDF LaTeX, 4 pages, 7 pdf figures. To appear in the proceedings of
the 16th International Conference in Quantum ChromoDynamics (QCD12), 2-6 July
2012, Montpellie
A piece of cake: the ground-state energies in gamma_i-deformed N=4 SYM theory
In the non-supersymmetric gamma_i-deformed N=4 SYM theory, the scaling
dimensions of the operators tr[Z^L] composed of L scalar fields Z receive
finite-size wrapping and prewrapping corrections in the 't Hooft limit. In this
paper, we calculate these scaling dimensions to leading wrapping order directly
from Feynman diagrams. For L>=3, the result is proportional to the maximally
transcendental `cake' integral. It matches with an earlier result obtained from
the integrability-based Luescher corrections, TBA and Y-system equations. At
L=2, where the integrability-based equations yield infinity, we find a finite
rational result. This result is renormalization-scheme dependent due to the
non-vanishing beta-function of an induced quartic scalar double-trace coupling,
on which we have reported earlier. This explicitly shows that conformal
invariance is broken - even in the 't Hooft limit.Comment: 21 pages, LaTeX, BibTeX, pstricks, feynm
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