180 research outputs found
On highest-energy state in the su(1|1) sector of N=4 super Yang-Mills theory
We consider the highest-energy state in the su(1|1) sector of N=4 super
Yang-Mills theory containing operators of the form tr(Z^{L-M} \psi^M) where Z
is a complex scalar and \psi is a component of gaugino. We show that this state
corresponds to the operator tr(\psi^L) and can be viewed as an analogue of the
antiferromagnetic state in the su(2) sector. We find perturbative expansions of
the energy of this state in both weak and strong 't Hooft coupling regimes
using asymptotic gauge theory Bethe ansatz equations. We also discuss a
possible analog of this state in the conjectured string Bethe ansatz equations.Comment: 23 pages, Late
On the Scattering Phase for AdS_5 x S^5 Strings
We propose a phase factor of the worldsheet S-matrix for strings on AdS_5 x
S^5 apparently solving Janik's crossing relation.Comment: 9 pages, v2: revised conclusions about agreement with perturbative
string theory; minor changes, v3: resolution to above problems indicated, to
appear in Mod. Phys. Lett.
Quantum corrections to the string Bethe ansatz
One-loop corrections to the energy of semiclassical rotating strings contain
both analytic and non-analytic terms in the 't Hooft coupling. Analytic
contributions agree with the prediction from the string Bethe ansatz based on
the classical S-matrix, but in order to include non-analytic contributions
quantum corrections are required. We find a general expression for the first
quantum correction to the string Bethe ansatz.Comment: 12 pages. Latex. v2: Misprints corrected and references adde
Two-loop AdS_5 x S^5 superstring: testing asymptotic Bethe ansatz and finite size corrections
We continue the investigation of two-loop string corrections to the energy of
a folded string with a spin S in AdS_5 and an angular momentum J in S^5, in the
scaling limit of large J and S with ell=pi J/(lambda^(1/2) ln S)=fixed. We
compute the generalized scaling function at two-loop order f_2(ell) both for
small and large values of ell matching the predictions based on the asymptotic
Bethe ansatz. In particular, in the small ell expansion, we derive an exact
integral form for the ell-dependent coefficient of the Catalan's constant term
in f_2(ell). Also, by resumming a certain subclass of multi-loop Feynman
diagrams we obtain an exact expression for the leading (ln ell) part of
f(lambda^(1/2), ell) which is valid to any order in the alpha'~1/lambda^(1/2)
expansion. At large ell the string energy has a BMN-like expansion and the
first few leading coefficients are expected to be the same at weak and at
strong coupling. We provide a new example of this non-renormalization for the
term which is generated at two loops in string theory and at one-loop in gauge
theory (sub-sub-leading in 1/J). We also derive a simple algebraic formula for
the term of maximal transcendentality in f_2(ell) expanded at large ell. In the
second part of the paper we initiate the study of 2-loop finite size
corrections to the string energy by formally compactifying the spatial
world-sheet direction in the string action expanded near long fast-spinning
string. We observe that the leading finite-size corrections are of "Casimir"
type coming from terms containing at least one massless propagator. We consider
in detail the one-loop order (reproducing the leading Landau-Lifshitz model
prediction) and then focus on the two-loop contributions to the (1/ln S) term
(for J=0). We find that in a certain regularization scheme used to discard
power divergences the two-loop coefficient of the (1/ln S) term appears to
vanish.Comment: 50 pages, 4 figures v2: typos corrected, references adde
Higher Loop Bethe Ansatz for Open Spin-Chains in AdS/CFT
We propose a perturbative asymptotic Bethe ansatz (PABA) for open spin-chain
systems whose Hamiltonians are given by matrices of anomalous dimension for
composite operators, and apply it to two types of composite operators related
to two different brane configurations. One is an AdS_4 \times S^2-brane in the
bulk AdS_5 \times S^5 which gives rise to a defect conformal field theory
(dCFT) in the dual field theory, and the other is a giant graviton system with
an open string excitation. In both cases, excitations on open strings attaching
to D-branes (a D5-brane for the dCFT case, and a spherical D3-brane for the
giant graviton case) can be represented by magnon states in the spin-chains
with appropriate boundary conditions, in which informations of the D-branes are
encoded. We concentrate on single-magnon problems, and explain how to calculate
boundary S-matrices via the PABA technique. We also discuss the energy spectrum
in the BMN limit.Comment: 1+24 pages, 1 figure, typos corrected, references added, discussions
on the integrability for giant gravitons modified, version to appear in JHE
Twisted K-Theory of Lie Groups
I determine the twisted K-theory of all compact simply connected simple Lie
groups. The computation reduces via the Freed-Hopkins-Teleman theorem to the
CFT prescription, and thus explains why it gives the correct result. Finally I
analyze the exceptions noted by Bouwknegt et al.Comment: 16 page
Decays of metastable vacua in SQCD
The decay rates of metastable SQCD vacua in ISS-type models, both towards
supersymmetric vacua as well as towards other nonsupersymmetric configurations
arising in theories with elementary spectators, are estimated numerically in
the semiclassical approximation by computing the corresponding multifield
bounce configurations. The scaling of the bounce action with respect to the
most relevant dimensionless couplings and ratios of scales is analyzed. In the
case of the decays towards the susy vacua generated by nonperturbative effects,
the results confirm previous analytical estimations of this scaling, obtained
by assuming a triangular potential barrier. The decay rates towards susy vacua
generated by R-symmetry breaking interactions turn out to be more than
sufficiently suppressed for the phenomenologically relevant parameter range,
and their behavior in this regime differs from analytic estimations valid for
parametrically small scale ratios. It is also shown that in models with
spectator fields, even though the decays towards vacua involving nonzero
spectator VEVs don't have a strong parametric dependence on the scale ratios,
the ISS vacuum can still be made long-lived in the presence of R-symmetry
breaking interactions.Comment: 22 pages, 7 figure
Uniform Light-Cone Gauge for Strings in AdS_5 x S^5: Solving su(1|1) Sector
We introduce a uniform light-cone gauge for strings propagating in AdS
space-time. We use the gauge to analyze strings from the su(1|1) sector, and
show that the reduced model is described by a quadratic action for two complex
fermions. Thus, the uniform light-cone gauge allows us to solve the model
exactly. We analyze the near BMN spectrum of states from the su(1|1) sector and
show that it correctly reproduces the 1/J corrections. We also compute the
spectrum in the strong coupling limit, and derive the famous \lambda^{1/4}
asymptotics. We then show that the same string spectrum can be also derived by
solving Bethe ansatz type equations, and discuss their relation to the quantum
string Bethe ansatz for the su(1|1) sector.Comment: 26 pages, Latex, v2: comparison to the strong coupling expansion of
the quantum string Bethe ansatz is added, discussion of the winding sector is
extended, references adde
Infinite spin limit of semiclassical string states
Motivated by recent works of Hofman and Maldacena and Dorey we consider a
special infinite spin limit of semiclassical spinning string states in AdS5 x
S5. We discuss examples of known folded and circular 2-spin string solutions
and demonstrate explicitly that the 1-loop superstring correction to the
classical expression for the energy vanishes in the limit when one of the spins
is much larger that the other. We also give a general discussion of this limit
at the level of integral equations describing finite gap solutions of the
string sigma model and argue that the corresponding asymptotic form of the
string and gauge Bethe equations is the same.Comment: 38 pages, 3 figures; v2: comments on derivation of bound states of
magnons from discrete Bethe equations added in section 4 and appendix C,
references added, Imperial-TP-AT-6-4, HUTP-06/A002
Integrability and Transcendentality
We derive the two-loop Bethe ansatz for the sl(2) twist operator sector of
N=4 gauge theory directly from the field theory. We then analyze a recently
proposed perturbative asymptotic all-loop Bethe ansatz in the limit of large
spacetime spin at large but finite twist, and find a novel all-loop scaling
function. This function obeys the Kotikov-Lipatov transcendentality principle
and does not depend on the twist. Under the assumption that one may extrapolate
back to leading twist, our result yields an all-loop prediction for the
large-spin anomalous dimensions of twist-two operators. The latter also appears
as an undetermined function in a recent conjecture of Bern, Dixon and Smirnov
for the all-loop structure of the maximally helicity violating (MHV) n-point
gluon amplitudes of N=4 gauge theory. This potentially establishes a direct
link between the worldsheet and the spacetime S-matrix approach. A further
assumption for the validity of our prediction is that perturbative BMN
(Berenstein-Maldacena-Nastase) scaling does not break down at four loops, or
beyond. We also discuss how the result gets modified if BMN scaling does break
down. Finally, we show that our result qualitatively agrees at strong coupling
with a prediction of string theory.Comment: 45 pages LaTeX, 3 postscript figures. v2: Chapter on BMN scaling and
transcendentality added. v3: version accepted for publication in JSTA
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