232 research outputs found
The complete one-loop dilatation operator of planar real beta-deformed N=4 SYM theory
We determine the missing finite-size corrections to the asymptotic one-loop
dilatation operator of the real -deformed SYM theory for
the gauge groups and in the 't Hooft limit. In the case,
the absence of the field components leads to a new kind of finite-size
effect, which we call prewrapping. We classify which states are potentially
affected by prewrapping at generic loop orders and comment on the necessity to
include it into the integrability-based description. As a further result, we
identify classes of -point correlation functions which at all loop orders in
the planar theory are given by the values of their undeformed counterparts.
Finally, we determine the superconformal multiplet structure and one-loop
anomalous dimensions of all single-trace states with classical scaling
dimension .Comment: Latex, feynmp, pstricks, 37 pages, 6 tables, v2: formulations
improved, references added, typos corrected, v3: typos corrected, matches
published versio
Quantum Symmetries and Marginal Deformations
We study the symmetries of the N=1 exactly marginal deformations of N=4 Super
Yang-Mills theory. For generic values of the parameters, these deformations are
known to break the SU(3) part of the R-symmetry group down to a discrete
subgroup. However, a closer look from the perspective of quantum groups reveals
that the Lagrangian is in fact invariant under a certain Hopf algebra which is
a non-standard quantum deformation of the algebra of functions on SU(3). Our
discussion is motivated by the desire to better understand why these theories
have significant differences from N=4 SYM regarding the planar integrability
(or rather lack thereof) of the spin chains encoding their spectrum. However,
our construction works at the level of the classical Lagrangian, without
relying on the language of spin chains. Our approach might eventually provide a
better understanding of the finiteness properties of these theories as well as
help in the construction of their AdS/CFT duals.Comment: 1+40 pages. v2: minor clarifications and references added. v3: Added
an appendix, fixed minor typo
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
Yangians in Deformed Super Yang-Mills Theories
We discuss the integrability structure of deformed, four-dimensional N=4
super Yang-Mills theories using Yangians. We employ a recent procedure by
Beisert and Roiban that generalizes the beta deformation of Lunin and Maldacena
to produce N=1 superconformal gauge theories, which have the superalgebra
SU(2,2|1)xU(1)xU(1). The deformed theories, including those with the more
general twist, were shown to have retained their integrable structure. Here we
examine the Yangian algebra of these deformed theories. In a five field
subsector, we compute the two cases of SU(2)xU(1)xU(1)xU(1) and
SU(2|1)xU(1)xU(1) as residual symmetries of SU(2,2|1)xU(1)xU(1). We compute a
twisted coproduct for these theories, and show that only for the residual
symmetry do we retain the standard coproduct. The twisted coproduct thus
provides a method for symmetry breaking. However, the full Yangian structure of
SU(2|3) is manifest in our subsector, albeit with twisted coproducts, and
provides for the integrability of the theory.Comment: 17 page
Four-loop anomalous dimensions in Leigh-Strassler deformations
We determine the scalar part of the four-loop chiral dilatation operator for
Leigh-Strassler deformations of N=4 super Yang-Mills. This is sufficient to
find the four-loop anomalous dimensions for operators in closed scalar
subsectors. This includes the SU(2) subsector of the (complex)
beta-deformation, where we explicitly compute the anomalous dimension for
operators with a single impurity. It also includes the "3-string null"
operators of the cubic Leigh-Strassler deformation. Our four-loop results show
that the rational part of the anomalous dimension is consistent with a
conjecture made in arXiv:1108.1583 based on the three-loop result of
arXiv:1008.3351 and the N=4 magnon dispersion relation. Here we find additional
zeta(3) terms.Comment: Latex, feynmp, 21 page
Long-Range GL(n) Integrable Spin Chains and Plane-Wave Matrix Theory
Quantum spin chains arise naturally from perturbative large-N field theories
and matrix models. The Hamiltonian of such a model is a long-range deformation
of nearest-neighbor type interactions. Here, we study the most general
long-range integrable spin chain with spins transforming in the fundamental
representation of gl(n). We derive the Hamiltonian and the corresponding
asymptotic Bethe ansatz at the leading four perturbative orders with several
free parameters. Furthermore, we propose Bethe equations for all orders and
identify the moduli of the integrable system. We finally apply our results to
plane-wave matrix theory and show that the Hamiltonian in a closed sector is
not of this form and therefore not integrable beyond the first perturbative
order. This also implies that the complete model is not integrable.Comment: 22 pages, v2: reference adde
Gauge-string duality for superconformal deformations of N=4 Super Yang-Mills theory
We analyze in detail the relation between an exactly marginal deformation of
N=4 SYM - the Leigh-Strassler or ``beta-deformation'' - and its string theory
dual (recently constructed in hep-th/0502086) by comparing energies of
semiclassical strings to anomalous dimensions of gauge-theory operators in the
two-scalar sector. We stress the existence of integrable structures on the two
sides of the duality. In particular, we argue that the integrability of strings
in AdS_5 x S^5 implies the integrability of the deformed world sheet theory
with real deformation parameter. We compare the fast string limit of the
worldsheet action in the sector with two angular momenta with the continuum
limit of the coherent state action of an anisotropic XXZ spin chain describing
the one-loop anomalous dimensions of the corresponding operators and find a
remarkable agreement for all values of the deformation parameter. We discuss
some of the properties of the Bethe Ansatz for this spin chain, solve the Bethe
equations for small number of excitations and comment on higher loop properties
of the dilatation operator. With the goal of going beyond the leading order in
the 't Hooft expansion we derive the analog of the Bethe equations on the
string-theory side, and show that they coincide with the thermodynamic limit of
the Bethe equations for the spin chain. We also compute the 1/J corrections to
the anomalous dimensions of operators with large R-charge (corresponding to
strings with angular momentum J) and match them to the 1-loop corrections to
the fast string energies. Our results suggest that the impressive agreement
between the gauge theory and semiclassical strings in AdS_5 x S^5 is part of a
larger picture underlying the gauge/gravity duality.Comment: 50 pages, Latex; v2:typos corrected, references added, clarifications
in sec 8 and Appendix A, a discussion of a rational solution added in section
4.2; v3: minor corrections to coefficients in eq. 2.5, 5.2 and appendix A;
v4: minor misprints correcte
Gauge-string duality for (non)supersymmetric deformations of N=4 Super Yang-Mills theory
We consider a non-supersymmetric example of the AdS/CFT duality which
generalizes the supersymmetric exactly marginal deformation constructed in
hep-th/0502086. The string theory background we use was found in hep-th/0503201
from the AdS_5 x S5 by a combination of T-dualities and shifts of angular
coordinates. It depends on three real parameters gamma_i which determine the
shape of the deformed 5-sphere. The dual gauge theory has the same field
content as N=4 SYM theory, but with scalar and Yukawa interactions ``deformed''
by gamma_i-dependent phases. The special case of equal deformation parameters
gamma_i=gamma corresponds to the N=1 supersymmetric deformation. We compare the
energies of semiclassical strings with three large angular momenta to the
1-loop anomalous dimensions of the corresponding gauge-theory scalar operators
and find that they match as it was the case in the SU(3) sector of the standard
AdS/CFT duality. In the supersymmetric case of equal gamma_i this extends the
result of our previous work (hep-th/0503192) from the 2-spin to the 3-spin
sector. This extension turns out to be quite nontrivial. To match the
corresponding low-energy effective ``Landau-Lifshitz'' actions on the string
theory and the gauge theory sides one is to make a special choice of the spin
chain Hamiltonian representing the 1-loop gauge theory dilatation operator.
This choice is adapted to low-energy approximation, i.e. it allows one to
capture the right vacuum states and the macroscopic spin wave sector of states
of the spin chain in the continuum coherent state effective action.Comment: 43 pages, Latex; v2:Discussion of 0-modes improved in section 2,
Appendix B expanded to demonstrate agreement between gauge and string theory
for 0-mode fluctuations; references added; v3: Modification to the discussion
on the U(1) factor in sec.4.
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